Code
source('dependencies.R')
knitr::opts_chunk$set(echo = TRUE, warning=FALSE, message=FALSE)
#install.packages("stargazer")
library(stargazer)Theresa Szczepanski
October 22, 2023
The Massachusetts Education Reform Act in 1993 was passed in the context of a national movement toward education reform throughout the United States. As early as 1989 there were calls to establish national curriculum standards as a way to improve student college and career readiness skills and close poverty gaps (Greer 2018). Massachusetts Comprehensive Assessment System (MCAS) tests were introduced as part of the Massachusetts Education Reform Act.
The MCAS tests are a significant tool for educational equity. Scores on the Grade 10 Math MCAS test “predict longer-term educational attainments and labor market success, above and beyond typical markers of student advantage” and differences among students are largely and “sometimes completely accounted for” by differences in 10th grade MCAS scores and educational attainments. (Papy 2020).
With the introduction of the new Common Core standards and accountability testing came the demand for aligned curricular materials and teaching practices. Research indicates that the choice of instructional materials can have an impact “as large as or larger than the impact of teacher quality” (Chingos 2012). Massachusetts, along with Arkansas, Delaware, Kentucky, Louisiana, Maryland, Mississippi, Nebraska, New Mexico, Ohio, Rhode Island, Tennessee, and Texas belongs to the Council of Chief State School Officers’ (CCSO), High Quality Instructional Materials and Professional Development network which aims to close the “opportunity gap” among students by ensuring that every teacher has access to high-quality, standards aligned instructional materials and receives relevant professional development to support their use of these materials (Chief State School Officers 2021).
All Massachusetts Public School students must complete a High School science MCAS exam providing a wealth of standardized data on students’ discipline specific skill development. All schools receive annual summary reports on student performance. Significant work has been done using the MCAS achievement data and the Student Opportunity Act to identify achievement gaps and address funding inequities across the Commonwealth (Papy 2020). With funding gaps outlined in the late 1990’s closing, one could consider how the MCAS data could be leveraged to support the state’s current high quality instructional materials initiatives. The state compiles school’s performance disaggregated by each MCAS question item (DESE 2022).
Using the curricular information provided in state wide Next Generation MCAS High School Introductory Physics Item reports together with school-level student performance data, we hope to address the following broad questions:
Is there a relationship between differences in a school’s performance across Science Practice Categories and a school’s overall achievement on the Introductory Physics exam?
How can trends in a school’s performance be used to provide schools with guidance on discipline-specific curricular areas to target to improve student achievement?
In this report, I will analyze the High School Introductory Physics Next Generation Massachusetts Comprehensive Assessment System (MCAS) tests results for Massachusetts public schools.
Data for the study were drawn from DESE’s Next Generation MCAS Test Achievement Results statewide report, Item Analysis statewide report, and the MCAS digital item library. The Next Generation High School Introductory Physics MCAS assessment consists of 42 multiple choice and constructed response items that assess students on Physical Science standards from the 2016 STE Massachusetts Curriculum Framework in the content Reporting Categories of Motions and Forces, MF, Energy, EN, and Waves, WA. Each item is associated with a specific content standard from the Massachusetts Curriculum Framework as well as an underlying science Practice Category of Evidence Reasoning and Modeling, ERM, Mathematics and Data, MD, or Investigations and Questioning, IQ. The State Item Report provides the percentage of points earned by students in a school for each item as well as the percentage of points earned by all students in the state for each item.
The HSPhy_NextGen_SchoolSum data frame contains summary performance results from 112 public schools across the commonwealth on the Next Generation High School Introductory Physics MCAS, which was administered in the Spring of 2022 and 2023. 87 schools tested students in both years and 25 schools only tested students in 1 of the 2 testing years, with 27,745 students completing the exam.
For each school, there are values reported for 44 different variables which consist of information from three broad categories
School Characteristics: This includes the name of the school and the size of the school, School Size, as determined by the number of students that completed the MCAS exam.
Discipline-Specifc Performance Metrics: This includes the percentage of points earned by students at a school for items each content Reporting Category, MF%, EN%, WA% and science Practice Category ERM%, MD%, IQ%, the difference between a school’s percentage of points earned compared to the percentage of points earned by all students in the state (MFDiff, ENDiff, etc…), and the variability in a school’s performance relative to the state by category as measured by the standard deviation of the school’s Diff across categories (SD MF Diff, SD EN Diff, etc…).
Aggregate Performance Level metrics: This includes a school’s percentage of students at each of the four Performance Levels, (E%: Exceeding Expectations, M%: Meeting Expectations, PM%: Partially Meeting Expectations, and NM%: Not Meeting Expectations), the difference between these percentages and the percentage of students in Massachusetts at each performance level (EDiff, MDiff, PMDiff, NMDiff), and an ordinal classification of school’s, EM Perf Stat based on the percentage of students that were classified as Exceeding or Meeting expectations on the exam (HighEM, HighM, Mid, Mid-Low, Low).
See the HSPhy_NextGenMCASDF data frame summary and codebook for further details about all variables.
A school’s percentage of students classified as Exceeding expectations on the Introductory Physics MCAS is negatively associated with a school’s variance in performance relative to students in the state on Mathematics and Data items, SD MD Diff.
A school’s summary performance on items in a given content Reporting Category as measured by MF%, EN%, and WA%, is positively associated with the Reporting Category's weight within the exam.
#HSPhy_NextGen_SchoolSum
HSPhy_NextGen_SchoolSum<-HSPhy_NextGen_SchoolSum%>%
ungroup()
#HSPhy_NextGen_SchoolSum
# HSPhy_NextGen_PerfDF
# HSPhy_NextGen_SchoolIT301DF
HSPhy_2023_SchoolSizeDF<-read_excel("data/2023_Physics_NextGenMCASItem.xlsx", skip = 1)%>%
select(`School Name`, `School Code`, `Tested`)%>%
mutate(`Tested` = as.integer(`Tested`))%>%
select(`School Name`, `School Code`, `Tested`)
HSPhy_2022_SchoolSizeDF<-read_excel("data/2022_Physics_NextGenMCASItem.xlsx", skip = 1)%>%
select(`School Name`, `School Code`, `Tested`)%>%
mutate(`Tested` = as.integer(`Tested`))%>%
select(`School Name`, `School Code`, `Tested`)
HSPhy_SchoolSize <- rbind(HSPhy_2023_SchoolSizeDF, HSPhy_2022_SchoolSizeDF)%>%
mutate(count = 1)%>%
group_by(`School Name`, `School Code`)%>%
summarise(count = sum(count),
`Tested` = sum(`Tested`))%>%
mutate(`Tested Count` = round(`Tested`/count))%>%
ungroup()
#HSPhy_SchoolSize
quantile <- quantile(HSPhy_SchoolSize$`Tested Count`)
HSPhy_Size<-HSPhy_SchoolSize%>%
mutate(`School Size` = case_when(
`Tested Count` <= quantile[2] ~ "Small",
`Tested Count` > quantile[2] &
`Tested Count` <= quantile[3] ~ "Low-Mid",
`Tested Count` > quantile[3] &
`Tested Count` <= quantile[4] ~ "Upper-Mid",
`Tested Count` > quantile[4] &
`Tested Count` <= quantile[5] ~ "Large",
))%>%
mutate(`School Size` = recode_factor(`School Size`,
"Small" = "Small",
"Low-Mid" = "Low-Mid",
"Upper-Mid" = "Upper-Mid",
"Large" = "Large",
.ordered = TRUE))%>%
select(`School Name`, `School Code`, `School Size`)
#HSPhy_Size
HSPhy_NextGen_SchoolSum<-HSPhy_NextGen_SchoolSum%>%
left_join(HSPhy_Size, by = c("School Name" = "School Name", "School Code" = "School Code"))%>%
mutate(`EMDiff` = `EDiff` + `MDiff`)%>%
mutate(`EM Perf Stat` = case_when(
`EDiff` > 0 & `EDiff` + `MDiff` > 0 ~ "HighEM",
`EDiff` <= 0 & `EDiff` + `MDiff` > 0 ~ "HighM",
#`EMDiff` > quantile(HSPhy_NextGen_SchoolSum$`EMDiff`)[3] &
`EMDiff` <= 0 & `EMDiff` > -14 ~ "Mid",
`EMDiff` <= -14 & `EMDiff` >= -33 ~ "Mid-Low",
`EMDiff` < -33 ~ "Low"
))%>%
mutate(`EM Perf Stat` = recode_factor(`EM Perf Stat`,
"HighEM" = "HighEM",
"HighM" = "HighM",
"Mid" = "Mid",
"Mid-Low" = "Mid-Low",
"Low" = "Low",
.ordered = TRUE))
HSPhy_NextGen_SchoolSum| Variable | Stats / Values | Freqs (% of Valid) | Graph | Missing | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Subject [character] | 1. PHY |
|
0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| School Name [character] |
|
|
0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| School Code [character] |
|
|
0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| EN% [numeric] |
|
50 distinct values | 0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| MF% [numeric] |
|
48 distinct values | 0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| WA% [numeric] |
|
47 distinct values | 0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| EN Diff SD [numeric] |
|
108 distinct values | 0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| MF Diff SD [numeric] |
|
106 distinct values | 0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| WA Diff SD [numeric] |
|
106 distinct values | 0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| IQ% [numeric] |
|
55 distinct values | 0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| MD% [numeric] |
|
48 distinct values | 0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| ERM% [numeric] |
|
49 distinct values | 0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| None% [numeric] |
|
48 distinct values | 0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| IQ Diff SD [numeric] |
|
66 distinct values | 10 (8.9%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| MD Diff SD [numeric] |
|
107 distinct values | 0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| ERM Diff SD [numeric] |
|
101 distinct values | 0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| None Diff SD [numeric] |
|
107 distinct values | 0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Tested Students [integer] |
|
95 distinct values | 0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| E% [numeric] |
|
29 distinct values | 0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| M% [numeric] |
|
50 distinct values | 0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| PM% [numeric] |
|
53 distinct values | 0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| NM% [numeric] |
|
44 distinct values | 0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| E%State [numeric] | 1 distinct value |
|
0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| M%State [numeric] | 1 distinct value |
|
0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| PM%State [numeric] | 1 distinct value |
|
0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| NM%State [numeric] | 1 distinct value |
|
0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| EDiff [numeric] |
|
29 distinct values | 0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| MDiff [numeric] |
|
50 distinct values | 0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| PMDiff [numeric] |
|
53 distinct values | 0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| NMDiff [numeric] |
|
44 distinct values | 0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| EN%State [numeric] | 1 distinct value |
|
0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| MF%State [numeric] | 1 distinct value |
|
0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| WA%State [numeric] | 1 distinct value |
|
0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| IQ%State [numeric] | 1 distinct value |
|
0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| MD%State [numeric] | 1 distinct value |
|
0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| ERM%State [numeric] | 1 distinct value |
|
0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| None%State [numeric] | 1 distinct value |
|
0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| School Size [ordered, factor] |
|
|
0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| EMDiff [numeric] |
|
64 distinct values | 0 (0.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| EM Perf Stat [ordered, factor] |
|
|
0 (0.0%) |
Generated by summarytools 1.0.1 (R version 4.2.2)
2023-11-19
To explore the relationship between the distribution of school’s students’ Performance Level and school’s performance in content categories, we examine the percentage of points earned by students at schools as well as the standard deviation of the difference between points earned by students at a school and points earned by students in the state across Reporting Categories and Practice Categories. We grouped schools by their EM Perf Stat, an ordinal variable classifying schools by the percentage of students they have that were classified as either Exceeding or Meeting expectations on the MCAS. These numbers seem to suggest that items classified with the Science Practice Category of Mathematics and Data seem to be more challenging to students than those classified as Evidence, Reasoning, and Modeling. These practice categories are strongly and equally emphasized within the exam; items tagged with these categories account for 82% of the available points on the exam with exactly 41% of available points coming from each category.
When considering content Reporting Categories, there do not seem to be discernible distinctions between EM Perf Stat and school’s achievement and performance across categories. All schools seem to perform the strongest on Motion and Forces items, followed by Energy, and weakest on Waves items. Notably, this is also the order of the relative weights of the content areas within the exam; MF, EN, and WA items account for 50%, 30%, and 20% of exam points respectively.
When examining the statewide performance distribution, we can see from the right-skew that it is rare for schools to have high percentages of students classified as Not Meeting expectations and even rarer for schools to have high percentages of students classified as Exceeding expectations.
HSPhy_NextGen_SchoolSum%>%
select(`E%`, `M%`, `PM%`, `NM%`)%>%
pivot_longer(c(1:4), names_to = "Performance Level", values_to = "% Students")%>%
ggplot( aes(x=`% Students`, color=`Performance Level`, fill=`Performance Level`)) +
geom_histogram(alpha=0.6, binwidth = 15) +
scale_fill_viridis(discrete=TRUE) +
scale_color_viridis(discrete=TRUE) +
#theme_ipsum() +
theme(
legend.position="none",
panel.spacing = unit(0.1, "lines"),
strip.text.x = element_text(size = 8)
) +
facet_wrap(~`Performance Level`)+
labs( y = "",
title = "School Performance Level Distribution",
x = "% Students at Performance Level",
caption = "NextGen HS Physics MCAS")Although Mathematics and Data and Evidence, Reasoning, and Modeling items have strong and equal weighting in the HS Introductory Physics exam, student performance distributions are noticeably different across these practice categories.
HSPhy_NextGen_SchoolSum%>%
select(`ERM%`, `MD%`)%>%
pivot_longer(c(1:2), names_to = "Practice Cat", values_to = "% Points")%>%
ggplot( aes(x=`% Points`, color=`Practice Cat`, fill=`Practice Cat`)) +
geom_histogram(alpha=0.6, binwidth = 3) +
scale_fill_viridis(discrete=TRUE) +
scale_color_viridis(discrete=TRUE) +
#theme_ipsum() +
theme(
panel.spacing = unit(0.1, "lines"),
strip.text.x = element_text(size = 8)
) +
facet_wrap(~`Practice Cat`)+
labs( y = "",
title = "School Performance by Practice Category",
x = "% Points Earned",
caption = "NextGen HS Physics MCAS")When considering the variability of a school’s performance on items relative to the state by Practice Category, SD MD Diff, and SD ERM Diff, we can see that Mathematics and Data is skewed more to the right.
HSPhy_NextGen_SchoolSum%>%
select(`ERM Diff SD`, `MD Diff SD`)%>%
pivot_longer(c(1:2), names_to = "Practice Cat", values_to = "SD Diff")%>%
ggplot( aes(x=`SD Diff`, color=`Practice Cat`, fill=`Practice Cat`)) +
geom_histogram(alpha=0.6, binwidth = 3) +
scale_fill_viridis(discrete=TRUE) +
scale_color_viridis(discrete=TRUE) +
# theme_ipsum() +
theme(
panel.spacing = unit(0.1, "lines"),
strip.text.x = element_text(size = 8)
) +
labs( y = "",
title = "School Performance Variation by Practice Category",
x = "SD Diff",
caption = "NextGen HS Physics MCAS") +
facet_wrap(~`Practice Cat`)These images, seem to suggest that schools with the highest percentage of students classified as Exceeding expectations on the MCAS have the lowest levels of variation in performance on Mathematics and Data Items and schools with the lowest percentage of students classified as Exceeding expectations on the MCAS have the highest levels of variation in performance on Mathematics and Data Items.
HSPhy_NextGen_SchoolSum%>%
select(`EM Perf Stat`, `ERM Diff SD`, `MD Diff SD` )%>%
pivot_longer(c(2:3), names_to = "Practice Cat", values_to = "SD Diff")%>%
ggplot( aes(x= `EM Perf Stat`, y=`SD Diff`, fill= `EM Perf Stat`)) +
geom_boxplot() +
scale_fill_viridis(discrete = TRUE, alpha=0.6) +
geom_jitter(color="black", size=0.4, alpha=0.9) +
theme(
plot.title = element_text(size=11),
axis.title.x=element_blank(),
#axis.text.x=element_blank()
) +
labs( y = "SD Diff",
title = "Student Performance Variation by Practice Category",
x = "",
caption = "NextGen HS Physics MCAS") +
facet_wrap(~`Practice Cat`)HSPhy_NextGen_SchoolSum%>%
select(`EM Perf Stat`, `ERM Diff SD`, `MD Diff SD` )%>%
pivot_longer(c(2:3), names_to = "Practice Cat", values_to = "SD Diff")%>%
ggplot( aes(x= `Practice Cat`, y=`SD Diff`, fill= `Practice Cat`)) +
geom_boxplot() +
scale_fill_viridis(discrete = TRUE, alpha=0.6) +
geom_jitter(color="black", size=0.4, alpha=0.9) +
#theme_ipsum() +
theme(
plot.title = element_text(size=11),
axis.title.x=element_blank(),
axis.text.x=element_blank()
) +
labs( y = "SD Diff",
title = "Student Practice Cat. Variation by Achievement Level",
x = "",
caption = "NextGen HS Physics MCAS") +
#xlab("")+
facet_wrap(~`EM Perf Stat`)These images, seem to suggest that students at all schools seem to have more difficulty with Mathematics and Data items as compared to Evidence, Reasoning, and Modeling Items.
HSPhy_NextGen_SchoolSum%>%
select(`EM Perf Stat`, `ERM%`, `MD%` )%>%
pivot_longer(c(2:3), names_to = "Practice Cat", values_to = "%Points")%>%
ggplot( aes(x= `EM Perf Stat`, y=`%Points`, fill= `EM Perf Stat`)) +
geom_boxplot() +
scale_fill_viridis(discrete = TRUE, alpha=0.6) +
geom_jitter(color="black", size=0.4, alpha=0.9) +
#theme_ipsum() +
theme(
plot.title = element_text(size=11)
) +
labs( y = "%Points Earned",
title = "Student Practice Cat. Achievement by Performance Level",
x = "",
caption = "NextGen HS Physics MCAS") +
#xlab("")+
facet_wrap(~`Practice Cat`)HSPhy_NextGen_SchoolSum%>%
select(`EM Perf Stat`, `ERM%`, `MD%` )%>%
pivot_longer(c(2:3), names_to = "Practice Cat", values_to = "%Points")%>%
ggplot( aes(x= `Practice Cat`, y=`%Points`, fill= `Practice Cat`)) +
geom_boxplot() +
scale_fill_viridis(discrete = TRUE, alpha=0.6) +
geom_jitter(color="black", size=0.4, alpha=0.9) +
#theme_ipsum() +
theme(
plot.title = element_text(size=11)
) +
labs( y = "%Points Earned",
title = "Student Practice Cat. Achievement by Performance Level",
x = "",
caption = "NextGen HS Physics MCAS") +
#xlab("")+
facet_wrap(~`EM Perf Stat`, scale ="free_y")# HSPhy_NextGen_SchoolSum%>%
# select(`EM Perf Stat`, `ERMDiff`, `MDDiff` )%>%
# pivot_longer(c(2:3), names_to = "Practice Cat", values_to = "%Points")%>%
# ggplot( aes(x= `EM Perf Stat`, y=`%Points`, fill= `EM Perf Stat`)) +
# geom_boxplot() +
# scale_fill_viridis(discrete = TRUE, alpha=0.6) +
# geom_jitter(color="black", size=0.4, alpha=0.9) +
# #theme_ipsum() +
# theme(
#
# plot.title = element_text(size=11)
# ) +
# labs( y = "%Points Earned",
# title = "Student Practice Cat. Achievement by Performance Level",
# x = "",
# caption = "NextGen HS Physics MCAS") +
# #xlab("")+
# facet_wrap(~`Practice Cat`)
# HSPhy_NextGen_SchoolSum%>%
# select(`EM Perf Stat`, `ERM%`, `MD%` )%>%
# pivot_longer(c(2:3), names_to = "Practice Cat", values_to = "%Points")%>%
# ggplot( aes(x= `Practice Cat`, y=`%Points`, fill= `Practice Cat`)) +
# geom_boxplot() +
# scale_fill_viridis(discrete = TRUE, alpha=0.6) +
# geom_jitter(color="black", size=0.4, alpha=0.9) +
# #theme_ipsum() +
# theme(
#
# plot.title = element_text(size=11)
# ) +
# labs( y = "%Points Earned",
# title = "Student Practice Cat. Achievement by Performance Level",
# x = "",
# caption = "NextGen HS Physics MCAS") +
# #xlab("")+
# facet_wrap(~`EM Perf Stat`, scale ="free_y")
# HSPhy_NextGen_SchoolSum %>%
# ggplot( aes(x= `EM Perf Stat`, y=`MD%`, fill= `EM Perf Stat`)) +
# geom_boxplot() +
# scale_fill_viridis(discrete = TRUE, alpha=0.6) +
# geom_jitter(color="black", size=0.4, alpha=0.9) +
# theme_ipsum() +
# theme(
# legend.position="none",
# plot.title = element_text(size=11)
# ) +
# ggtitle("A boxplot with jitter") +
# xlab("")
# HSPhy_NextGen_SchoolSum %>%
# ggplot( aes(x= `EM Perf Stat`, y=`MD Diff SD`, fill= `EM Perf Stat`)) +
# geom_boxplot() +
# scale_fill_viridis(discrete = TRUE, alpha=0.6) +
# geom_jitter(color="black", size=0.4, alpha=0.9) +
# theme_ipsum() +
# theme(
# legend.position="none",
# plot.title = element_text(size=11)
# ) +
# ggtitle("A boxplot with jitter") +
# xlab("")
#
# HSPhy_NextGen_SchoolSum %>%
# ggplot( aes(x= `EM Perf Stat`, y=`ERM Diff SD`, fill= `EM Perf Stat`)) +
# geom_boxplot() +
# scale_fill_viridis(discrete = TRUE, alpha=0.6) +
# geom_jitter(color="black", size=0.4, alpha=0.9) +
# theme_ipsum() +
# theme(
# legend.position="none",
# plot.title = element_text(size=11)
# ) +
# ggtitle("A boxplot with jitter") +
# xlab("")
#
# HSPhy_NextGen_SchoolSum %>%
# ggplot( aes(x= `EM Perf Stat`, y=`ERM%`, fill= `EM Perf Stat`)) +
# geom_boxplot() +
# scale_fill_viridis(discrete = TRUE, alpha=0.6) +
# geom_jitter(color="black", size=0.4, alpha=0.9) +
# theme_ipsum() +
# theme(
# legend.position="none",
# plot.title = element_text(size=11)
# ) +
# ggtitle("A boxplot with jitter") +
# xlab("")Here we can visualize the variability of a school’s performance on items partitioned by Content Reporting Category of Motion and Forces, Energy, and Waves via: MF%/SD MF Diff, EN%/SD EN Diff, and WA%/SD WA Diff.
HSPhy_NextGen_SchoolSum%>%
select(`EM Perf Stat`, `MF Diff SD`, `EN Diff SD`, `WA Diff SD` )%>%
pivot_longer(c(2:4), names_to = "Report Cat", values_to = "SD Diff")%>%
ggplot( aes(x=`SD Diff`, color=`Report Cat`, fill=`Report Cat`)) +
geom_histogram(alpha=0.6, binwidth = 3) +
scale_fill_viridis(discrete=TRUE) +
scale_color_viridis(discrete=TRUE) +
#theme_ipsum() +
theme(
panel.spacing = unit(0.1, "lines"),
strip.text.x = element_text(size = 8)
) +
labs( y = "",
title = "School Performance Variation by Content Reporting Category",
x = "SD Diff",
caption = "NextGen HS Physics MCAS") +
facet_wrap(~`Report Cat`)HSPhy_NextGen_SchoolSum%>%
select(`EM Perf Stat`, `MF%`, `EN%`, `WA%` )%>%
pivot_longer(c(2:4), names_to = "Report Cat", values_to = "% Points")%>%
ggplot( aes(x=`% Points`, color=`Report Cat`, fill=`Report Cat`)) +
geom_histogram(alpha=0.6, binwidth = 3) +
scale_fill_viridis(discrete=TRUE) +
scale_color_viridis(discrete=TRUE) +
#theme_ipsum() +
theme(
panel.spacing = unit(0.1, "lines"),
strip.text.x = element_text(size = 8)
) +
facet_wrap(~`Report Cat`)+
labs( y = "",
title = "Student Performance by Content Reporting Category",
x = "% Points Earned",
caption = "NextGen HS Physics MCAS")These images suggest that most schools exhibit similar levels of variability in performance relative to the state across all reporting categories. Schools with the lowest percentage of students Exceeding expectations exhibit high variability in performance across all content reporting categories, but seem to have lower variability on Waves items.
HSPhy_NextGen_SchoolSum%>%
select(`EM Perf Stat`, `MF Diff SD`, `EN Diff SD`, `WA Diff SD` )%>%
pivot_longer(c(2:4), names_to = "Report Cat", values_to = "SD Diff")%>%
ggplot( aes(x= `EM Perf Stat`, y=`SD Diff`, fill= `EM Perf Stat`)) +
geom_boxplot() +
scale_fill_viridis(discrete = TRUE, alpha=0.6) +
geom_jitter(color="black", size=0.4, alpha=0.9) +
theme(
plot.title = element_text(size=11),
axis.title.x=element_blank(),
axis.text.x=element_blank()
) +
labs( y = "SD Diff",
title = "School Performance Variation by Content Reporting Category",
x = "",
caption = "NextGen HS Physics MCAS") +
facet_wrap(~`Report Cat`)HSPhy_NextGen_SchoolSum%>%
select(`EM Perf Stat`, `MF Diff SD`, `EN Diff SD`, `WA Diff SD` )%>%
pivot_longer(c(2:4), names_to = "Report Cat", values_to = "SD Diff")%>%
ggplot( aes(x= `Report Cat`, y=`SD Diff`, fill= `Report Cat`)) +
geom_boxplot() +
scale_fill_viridis(discrete = TRUE, alpha=0.6) +
geom_jitter(color="black", size=0.4, alpha=0.9) +
#theme_ipsum() +
theme(
plot.title = element_text(size=11),
axis.title.x=element_blank(),
axis.text.x=element_blank()
) +
labs( y = "SD Diff",
title = "School Content Reporting Cat. Variation by Achievement Level",
x = "",
caption = "NextGen HS Physics MCAS") +
#xlab("")+
facet_wrap(~`EM Perf Stat`)HSPhy_NextGen_SchoolSum%>%
select(`EM Perf Stat`, `MF%`, `EN%`, `WA%` )%>%
pivot_longer(c(2:4), names_to = "Report Cat", values_to = "% Points")%>%
ggplot( aes(x= `Report Cat`, y=`% Points`, fill= `Report Cat`)) +
geom_boxplot() +
scale_fill_viridis(discrete = TRUE, alpha=0.6) +
geom_jitter(color="black", size=0.4, alpha=0.9) +
#theme_ipsum() +
theme(
plot.title = element_text(size=11),
axis.title.x=element_blank(),
axis.text.x=element_blank()
) +
labs( y = "Report Cat%",
title = "School Content Reporting Cat. Performance by Achievement Level",
x = "",
caption = "NextGen HS Physics MCAS") +
#xlab("")+
facet_wrap(~`EM Perf Stat`)# HSPhy_NextGen_SchoolSum %>%
# ggplot( aes(x= `EM Perf Stat`, y=`MF%`, fill= `EM Perf Stat`)) +
# geom_boxplot() +
# scale_fill_viridis(discrete = TRUE, alpha=0.6) +
# geom_jitter(color="black", size=0.4, alpha=0.9) +
# theme_ipsum() +
# theme(
# legend.position="none",
# plot.title = element_text(size=11)
# ) +
# ggtitle("A boxplot with jitter") +
# xlab("")
#
# HSPhy_NextGen_SchoolSum %>%
# ggplot( aes(x= `EM Perf Stat`, y=`MF Diff SD`, fill= `EM Perf Stat`)) +
# geom_boxplot() +
# scale_fill_viridis(discrete = TRUE, alpha=0.6) +
# geom_jitter(color="black", size=0.4, alpha=0.9) +
# theme_ipsum() +
# theme(
# legend.position="none",
# plot.title = element_text(size=11)
# ) +
# ggtitle("A boxplot with jitter") +
# xlab("")
#
#
#
# HSPhy_NextGen_SchoolSum %>%
# ggplot( aes(x= `EM Perf Stat`, y=`EN%`, fill= `EM Perf Stat`)) +
# geom_boxplot() +
# scale_fill_viridis(discrete = TRUE, alpha=0.6) +
# geom_jitter(color="black", size=0.4, alpha=0.9) +
# theme_ipsum() +
# theme(
# legend.position="none",
# plot.title = element_text(size=11)
# ) +
# ggtitle("A boxplot with jitter") +
# xlab("")
#
# HSPhy_NextGen_SchoolSum %>%
# ggplot( aes(x= `EM Perf Stat`, y=`EN Diff SD`, fill= `EM Perf Stat`)) +
# geom_boxplot() +
# scale_fill_viridis(discrete = TRUE, alpha=0.6) +
# geom_jitter(color="black", size=0.4, alpha=0.9) +
# theme_ipsum() +
# theme(
# legend.position="none",
# plot.title = element_text(size=11)
# ) +
# ggtitle("A boxplot with jitter") +
# xlab("")
#
# HSPhy_NextGen_SchoolSum %>%
# ggplot( aes(x= `EM Perf Stat`, y=`WA%`, fill= `EM Perf Stat`)) +
# geom_boxplot() +
# scale_fill_viridis(discrete = TRUE, alpha=0.6) +
# geom_jitter(color="black", size=0.4, alpha=0.9) +
# theme_ipsum() +
# theme(
# legend.position="none",
# plot.title = element_text(size=11)
# ) +
# ggtitle("A boxplot with jitter") +
# xlab("")
#
# HSPhy_NextGen_SchoolSum %>%
# ggplot( aes(x= `EM Perf Stat`, y=`WA Diff SD`, fill= `EM Perf Stat`)) +
# geom_boxplot() +
# scale_fill_viridis(discrete = TRUE, alpha=0.6) +
# geom_jitter(color="black", size=0.4, alpha=0.9) +
# theme_ipsum() +
# theme(
# legend.position="none",
# plot.title = element_text(size=11)
# ) +
# ggtitle("A boxplot with jitter") +
# xlab("")Exceeding or Meeting expectations on the Introductory Physics MCAS is negatively associated with a school’s variance in performance relative to students in the state on Mathematics and Data items, SD MD Diff.To explore the relationship between the variance in a schools’ Diff compared to the state on Mathematics and Data items, MD Diff SD and a school’s percentage of students meeting or exceeding expectations on the MCAS, EorM%, we ran a few Hypothesis tests. We considered the impact of the variability in Evidence, Reasoning, and Modeling, ERM Diff SD, and School Size as controls. From our table, there appears to be a relationship between School Size. It appears that Small schools have a higher variation in mathematics and data items and typically perform worse on Mathematics and Data and overall on the MCAS compared to larger schools.
HSPhy_NextGen_SchoolSum%>%
select(`School Size`, `MD Diff SD`, `ERM Diff SD` )%>%
pivot_longer(c(2:3), names_to = "Practice Cat", values_to = "SD Diff")%>%
ggplot( aes(x= `Practice Cat`, y=`SD Diff`, fill= `Practice Cat`)) +
geom_boxplot() +
scale_fill_viridis(discrete = TRUE, alpha=0.6) +
geom_jitter(color="black", size=0.4, alpha=0.9) +
#theme_ipsum() +
theme(
plot.title = element_text(size=11),
axis.title.x=element_blank(),
axis.text.x=element_blank()
) +
labs( y = "SD Diff",
title = "Student Practice Cat. Variation by School Size",
x = "",
caption = "NextGen HS Physics MCAS") +
#xlab("")+
facet_wrap(~`School Size`, scale = "free")HSPhy_NextGen_SchoolSum%>%
select(`School Size`, `MD%`, `ERM%` )%>%
pivot_longer(c(2:3), names_to = "Practice Cat", values_to = "%Points")%>%
ggplot( aes(x= `Practice Cat`, y=`%Points`, fill= `Practice Cat`)) +
geom_boxplot() +
scale_fill_viridis(discrete = TRUE, alpha=0.6) +
geom_jitter(color="black", size=0.4, alpha=0.9) +
#theme_ipsum() +
theme(
plot.title = element_text(size=11),
axis.title.x=element_blank(),
axis.text.x=element_blank()
) +
labs( y = "% Points Earned",
title = "Student Practice Cat. Achievement by School Size",
x = "",
caption = "NextGen HS Physics MCAS") +
#xlab("")+
facet_wrap(~`School Size`)However, when you group the schools by EM Perf Stat, you find that the highest performing, High EM, Small schools have a higher percentage of students meeting or exceeding expectations.
Across all sizes, it seems that the weakest performing schools have more variation in mathematics and data and the strongest performing schools have less variability in Mathematics and Data than in Evidence, Reasoning, and Modeling.
HSPhy_NextGen_SchoolSum%>%
select(`School Size`, `EorM%`, `MD Diff SD`, `EM Perf Stat` )%>%
#pivot_longer(c(2:3), names_to = "Practice Cat", values_to = "SD Diff")%>%
ggplot( aes(x= `School Size`, y=`EorM%`, fill= `School Size`)) +
geom_boxplot() +
scale_fill_viridis(discrete = TRUE, alpha=0.6) +
geom_jitter(color="black", size=0.4, alpha=0.9) +
#theme_ipsum() +
theme(
plot.title = element_text(size=11),
axis.title.x=element_blank(),
axis.text.x=element_blank()
) +
labs( y = "SD Diff",
title = "Students Meeting or Exceeding Expectations . Variation by Achievement Level",
x = "",
caption = "NextGen HS Physics MCAS") +
#xlab("")+
facet_wrap(~`EM Perf Stat`, scales = "free")ANOVA_MD_size <- aov(`MD Diff SD` ~ `EM Perf Stat` + `School Size`, data=HSPhy_NextGen_SchoolSum)
ANOVA_MD_interact <- aov(`MD Diff SD` ~ `EM Perf Stat` + `School Size` + `EM Perf Stat` * `School Size`, data=HSPhy_NextGen_SchoolSum)
ANOVA_EorM_MD<- aov(`EorM%` ~ `MD Diff SD` + `School Size`, data=HSPhy_NextGen_SchoolSum)
ANOVA_EorM_interact_MD <- aov(`EorM%` ~ `MD Diff SD` + `School Size` + `MD Diff SD` * `School Size`, data=HSPhy_NextGen_SchoolSum)
summary(ANOVA_MD_size) Df Sum Sq Mean Sq F value Pr(>F)
`EM Perf Stat` 4 642.5 160.6 44.58 < 2e-16 ***
`School Size` 3 356.6 118.8 32.99 4.58e-15 ***
Residuals 104 374.7 3.6
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Df Sum Sq Mean Sq F value Pr(>F)
`EM Perf Stat` 4 642.5 160.62 43.056 < 2e-16 ***
`School Size` 3 356.6 118.85 31.860 2.95e-14 ***
`EM Perf Stat`:`School Size` 11 27.7 2.52 0.676 0.758
Residuals 93 346.9 3.73
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Df Sum Sq Mean Sq F value Pr(>F)
`MD Diff SD` 1 21623 21623 44.558 1.13e-09 ***
`School Size` 3 4794 1598 3.293 0.0234 *
Residuals 107 51924 485
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Df Sum Sq Mean Sq F value Pr(>F)
`MD Diff SD` 1 21623 21623 46.446 6.32e-10 ***
`School Size` 3 4794 1598 3.433 0.0197 *
`MD Diff SD`:`School Size` 3 3507 1169 2.511 0.0627 .
Residuals 104 48417 466
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Df Sum Sq Mean Sq F value Pr(>F)
`EM Perf Stat` 4 311.8 77.95 13.33 7.58e-09 ***
Residuals 107 625.7 5.85
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Df Sum Sq Mean Sq F value Pr(>F)
`EM Perf Stat` 4 311.8 77.95 33.61 <2e-16 ***
`School Size` 3 384.5 128.18 55.28 <2e-16 ***
Residuals 104 241.2 2.32
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Df Sum Sq Mean Sq F value Pr(>F)
`ERM Diff SD` 1 15815 15815 28.531 5.23e-07 ***
`School Size` 3 3216 1072 1.934 0.128
Residuals 107 59310 554
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Df Sum Sq Mean Sq F value Pr(>F)
`ERM Diff SD` 1 15815 15815 28.561 5.4e-07 ***
`School Size` 3 3216 1072 1.936 0.128
`ERM Diff SD`:`School Size` 3 1722 574 1.037 0.380
Residuals 104 57588 554
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Df Sum Sq Mean Sq F value Pr(>F)
`MD Diff SD` 1 21623 21623 41.577 3.19e-09 ***
`ERM Diff SD` 1 31 31 0.059 0.809
Residuals 109 56688 520
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
HSPhy_NextGen_SchoolSum_Diff<-HSPhy_NextGen_SchoolSum %>%
select(`EM Perf Stat`, `ERM Diff SD`, `MD Diff SD` )%>%
pivot_longer(c(2:3), names_to = "Practice Cat", values_to = "SD Diff")%>%
group_by(`Practice Cat`, `EM Perf Stat`)%>%
summarize(`SD SD Diff` = sd(`SD Diff`, na.rm = TRUE),
`Mean SD Diff` = mean(`SD Diff`, na.rm = TRUE))%>%
ungroup()
test1 <- HSPhy_NextGen_SchoolSum_Diff%>%
select(`Practice Cat`, `SD SD Diff`)
t.test( test1$`SD SD Diff` ~ test1$`Practice Cat`, paired = TRUE)
Paired t-test
data: test1$`SD SD Diff` by test1$`Practice Cat`
t = -0.1841, df = 4, p-value = 0.8629
alternative hypothesis: true mean difference is not equal to 0
95 percent confidence interval:
-1.0982164 0.9616354
sample estimates:
mean difference
-0.06829049
test2<-HSPhy_NextGen_SchoolSum %>%
select(`School Name`, `EM Perf Stat`, `School Size`, `ERM Diff SD`, `MD Diff SD` )%>%
pivot_longer(c(4:5), names_to = "Practice Cat", values_to = "SD Diff")%>%
filter(`EM Perf Stat` == "HighEM" | `EM Perf Stat` == "Mid")
## filtered for High Performing Schools
test2
Paired t-test
data: test2$`SD Diff` by test2$`Practice Cat`
t = 2.7086, df = 39, p-value = 0.009983
alternative hypothesis: true mean difference is not equal to 0
95 percent confidence interval:
0.130287 0.898713
sample estimates:
mean difference
0.5145
Paired t-test
data: test3$`SD Diff` by test3$`Practice Cat`
t = -2.4286, df = 23, p-value = 0.02338
alternative hypothesis: true mean difference is not equal to 0
95 percent confidence interval:
-2.6033031 -0.2083636
sample estimates:
mean difference
-1.405833
Reporting Category as measured by MF%, EN%, and WA%, is positively associated with the Reporting Category's weight within the exam. Df Sum Sq Mean Sq F value Pr(>F)
`EM Perf Stat` 4 137.6 34.39 4.802 0.00133 **
Residuals 107 766.4 7.16
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Df Sum Sq Mean Sq F value Pr(>F)
`EM Perf Stat` 4 446.3 111.57 14.7 1.32e-09 ***
Residuals 107 811.8 7.59
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Df Sum Sq Mean Sq F value Pr(>F)
`EM Perf Stat` 4 447.2 111.79 19.59 4.02e-12 ***
Residuals 107 610.5 5.71
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
HSPhy_NextGen_SchoolSum%>%
select(`EM Perf Stat`, `ERM Diff SD`, `MD Diff SD` )%>%
pivot_longer(c(2:3), names_to = "Practice Cat", values_to = "SD Diff")%>%
group_by(`Practice Cat`, `EM Perf Stat`)%>%
summarize(`SD SD Diff` = sd(`SD Diff`, na.rm = TRUE),
`Mean SD Diff` = mean(`SD Diff`, na.rm = TRUE))
Call:
lm(formula = `EorM%` ~ (`MD Diff SD`), data = HSPhy_NextGen_SchoolSum)
Residuals:
Min 1Q Median 3Q Max
-32.575 -18.347 -4.778 15.525 81.212
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 73.1813 5.6876 12.867 < 2e-16 ***
`MD Diff SD` -3.9674 0.6127 -6.476 2.73e-09 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 22.71 on 110 degrees of freedom
Multiple R-squared: 0.276, Adjusted R-squared: 0.2694
F-statistic: 41.94 on 1 and 110 DF, p-value: 2.726e-09
This states that MD is significant but ERM is not statistically significant?
Call:
lm(formula = `EorM%` ~ (`ERM Diff SD` + `MD Diff SD`), data = HSPhy_NextGen_SchoolSum)
Residuals:
Min 1Q Median 3Q Max
-32.499 -18.077 -4.584 16.254 81.167
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 74.0590 6.7612 10.953 < 2e-16 ***
`ERM Diff SD` -0.3279 1.3517 -0.243 0.80876
`MD Diff SD` -3.7413 1.1166 -3.351 0.00111 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 22.81 on 109 degrees of freedom
Multiple R-squared: 0.2764, Adjusted R-squared: 0.2631
F-statistic: 20.82 on 2 and 109 DF, p-value: 2.201e-08
Call:
lm(formula = `EorM%` ~ (`EN Diff SD`), data = HSPhy_NextGen_SchoolSum)
Residuals:
Min 1Q Median 3Q Max
-33.548 -18.356 -4.079 14.269 80.867
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 70.0957 6.1134 11.466 < 2e-16 ***
`EN Diff SD` -3.6402 0.6676 -5.453 3.07e-07 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 23.68 on 110 degrees of freedom
Multiple R-squared: 0.2128, Adjusted R-squared: 0.2056
F-statistic: 29.74 on 1 and 110 DF, p-value: 3.073e-07
Call:
lm(formula = `EorM%` ~ (`MF Diff SD`), data = HSPhy_NextGen_SchoolSum)
Residuals:
Min 1Q Median 3Q Max
-31.602 -19.591 -3.146 13.321 82.578
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 78.6411 6.4338 12.223 < 2e-16 ***
`MF Diff SD` -4.5448 0.6968 -6.522 2.18e-09 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 22.66 on 110 degrees of freedom
Multiple R-squared: 0.2789, Adjusted R-squared: 0.2723
F-statistic: 42.54 on 1 and 110 DF, p-value: 2.182e-09
Call:
lm(formula = `EorM%` ~ (`WA Diff SD`), data = HSPhy_NextGen_SchoolSum)
Residuals:
Min 1Q Median 3Q Max
-46.473 -21.430 -1.154 16.703 79.358
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 62.9282 7.4207 8.480 1.15e-13 ***
`WA Diff SD` -2.8688 0.8444 -3.397 0.000948 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 25.39 on 110 degrees of freedom
Multiple R-squared: 0.09496, Adjusted R-squared: 0.08673
F-statistic: 11.54 on 1 and 110 DF, p-value: 0.0009481
Call:
lm(formula = `EorM%` ~ (`MF Diff SD`) + `EN Diff SD` + `MF Diff SD` *
`EN Diff SD`, data = HSPhy_NextGen_SchoolSum)
Residuals:
Min 1Q Median 3Q Max
-31.095 -19.080 -3.607 13.209 82.025
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 88.5460 15.4514 5.731 9.16e-08 ***
`MF Diff SD` -5.1276 1.9197 -2.671 0.00873 **
`EN Diff SD` -1.6326 2.1240 -0.769 0.44380
`MF Diff SD`:`EN Diff SD` 0.1096 0.1584 0.692 0.49069
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 22.81 on 108 degrees of freedom
Multiple R-squared: 0.2829, Adjusted R-squared: 0.2629
F-statistic: 14.2 on 3 and 108 DF, p-value: 7.241e-08
Call:
lm(formula = `EorM%` ~ (`MF Diff SD`) + `WA Diff SD` + `MF Diff SD` *
`WA Diff SD`, data = HSPhy_NextGen_SchoolSum)
Residuals:
Min 1Q Median 3Q Max
-30.132 -18.281 -4.656 13.137 78.167
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 91.2521 20.3203 4.491 1.79e-05 ***
`MF Diff SD` -7.6468 2.4499 -3.121 0.00231 **
`WA Diff SD` -0.2917 2.5515 -0.114 0.90919
`MF Diff SD`:`WA Diff SD` 0.2133 0.2450 0.871 0.38595
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 22.55 on 108 degrees of freedom
Multiple R-squared: 0.299, Adjusted R-squared: 0.2795
F-statistic: 15.35 on 3 and 108 DF, p-value: 2.181e-08
Call:
lm(formula = `EorM%` ~ (`MD Diff SD`) + `WA Diff SD` + `MD Diff SD` *
`WA Diff SD`, data = HSPhy_NextGen_SchoolSum)
Residuals:
Min 1Q Median 3Q Max
-33.160 -16.523 -5.964 14.101 69.660
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 104.1191 18.7929 5.540 2.15e-07 ***
`MD Diff SD` -10.0194 2.5033 -4.002 0.000115 ***
`WA Diff SD` -1.7848 2.1050 -0.848 0.398373
`MD Diff SD`:`WA Diff SD` 0.4548 0.2177 2.089 0.039048 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 22.18 on 108 degrees of freedom
Multiple R-squared: 0.3218, Adjusted R-squared: 0.303
F-statistic: 17.09 on 3 and 108 DF, p-value: 3.762e-09
Call:
lm(formula = `EorM%` ~ (`MD Diff SD`) + `MF Diff SD` + `MD Diff SD` *
`MF Diff SD`, data = HSPhy_NextGen_SchoolSum)
Residuals:
Min 1Q Median 3Q Max
-32.536 -16.951 -4.496 12.527 83.141
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 92.7357 14.3853 6.447 3.29e-09 ***
`MD Diff SD` -4.5226 2.6891 -1.682 0.0955 .
`MF Diff SD` -3.3337 1.9103 -1.745 0.0838 .
`MD Diff SD`:`MF Diff SD` 0.1680 0.1427 1.178 0.2415
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 22.57 on 108 degrees of freedom
Multiple R-squared: 0.298, Adjusted R-squared: 0.2785
F-statistic: 15.28 on 3 and 108 DF, p-value: 2.35e-08
Call:
lm(formula = `EorM%` ~ (`MD Diff SD`) + `EN Diff SD` + `MD Diff SD` *
`EN Diff SD`, data = HSPhy_NextGen_SchoolSum)
Residuals:
Min 1Q Median 3Q Max
-34.020 -17.378 -4.997 12.832 86.410
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 90.9327 13.8560 6.563 1.89e-09 ***
`MD Diff SD` -6.4081 2.1149 -3.030 0.00306 **
`EN Diff SD` -1.4283 1.7193 -0.831 0.40797
`MD Diff SD`:`EN Diff SD` 0.1842 0.1292 1.426 0.15687
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 22.7 on 108 degrees of freedom
Multiple R-squared: 0.2894, Adjusted R-squared: 0.2697
F-statistic: 14.66 on 3 and 108 DF, p-value: 4.462e-08
Call:
lm(formula = `EorM%` ~ `MD%` + `ERM%` + `MD%` * `ERM%`, data = HSPhy_NextGen_SchoolSum)
Residuals:
Min 1Q Median 3Q Max
-18.9971 -2.5815 0.1229 2.3757 16.8436
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -31.643553 5.538802 -5.713 9.92e-08 ***
`MD%` 0.801079 0.206932 3.871 0.000186 ***
`ERM%` 0.148625 0.203262 0.731 0.466240
`MD%`:`ERM%` 0.009329 0.002118 4.404 2.51e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 4.473 on 108 degrees of freedom
Multiple R-squared: 0.9724, Adjusted R-squared: 0.9717
F-statistic: 1269 on 3 and 108 DF, p-value: < 2.2e-16
Call:
lm(formula = `EorM%` ~ `MD%` + `WA%` + `MD%` * `WA%`, data = HSPhy_NextGen_SchoolSum)
Residuals:
Min 1Q Median 3Q Max
-17.1752 -3.0657 -0.1061 2.2054 19.8722
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -35.163765 4.730111 -7.434 2.63e-11 ***
`MD%` 1.290583 0.161619 7.985 1.63e-12 ***
`WA%` -0.015233 0.205137 -0.074 0.94094
`MD%`:`WA%` 0.006053 0.002141 2.828 0.00559 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 4.729 on 108 degrees of freedom
Multiple R-squared: 0.9692, Adjusted R-squared: 0.9683
F-statistic: 1132 on 3 and 108 DF, p-value: < 2.2e-16
Call:
lm(formula = `EorM%` ~ `ERM%` + `WA%` + `ERM%` * `WA%`, data = HSPhy_NextGen_SchoolSum)
Residuals:
Min 1Q Median 3Q Max
-16.8575 -3.3910 0.0816 2.9314 13.5817
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -46.744066 6.471302 -7.223 7.53e-11 ***
`ERM%` 0.993748 0.175196 5.672 1.19e-07 ***
`WA%` 0.315195 0.227940 1.383 0.170
`ERM%`:`WA%` 0.007465 0.002715 2.749 0.007 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 5.197 on 108 degrees of freedom
Multiple R-squared: 0.9628, Adjusted R-squared: 0.9617
F-statistic: 931 on 3 and 108 DF, p-value: < 2.2e-16
Call:
lm(formula = `EorM%` ~ `ERM%` + `MD%` + `MF%` + `MD%` * `ERM%` +
`MD%` * `MF%` + `ERM%` * `MF%`, data = HSPhy_NextGen_SchoolSum)
Residuals:
Min 1Q Median 3Q Max
-14.4908 -2.3554 0.2093 1.9293 14.2689
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -19.38914 9.12900 -2.124 0.036026 *
`ERM%` 1.37435 0.84576 1.625 0.107162
`MD%` 4.55083 0.89029 5.112 1.44e-06 ***
`MF%` -5.12934 1.11268 -4.610 1.14e-05 ***
`ERM%`:`MD%` -0.07223 0.02178 -3.317 0.001251 **
`MD%`:`MF%` 0.01931 0.01667 1.158 0.249291
`ERM%`:`MF%` 0.06161 0.01704 3.616 0.000461 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 4.083 on 105 degrees of freedom
Multiple R-squared: 0.9777, Adjusted R-squared: 0.9764
F-statistic: 765.9 on 6 and 105 DF, p-value: < 2.2e-16
Call:
lm(formula = `EorM%` ~ `ERM%` + `MD%` + `WA%` + `MD%` * `ERM%` +
`MD%` * `WA%` + `ERM%` * `WA%`, data = HSPhy_NextGen_SchoolSum)
Residuals:
Min 1Q Median 3Q Max
-15.1584 -2.1387 0.2441 2.1956 14.8754
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -27.02886 8.91137 -3.033 0.00305 **
`ERM%` -0.79907 0.62833 -1.272 0.20628
`MD%` -0.73390 0.89506 -0.820 0.41410
`WA%` 2.44743 0.76083 3.217 0.00172 **
`ERM%`:`MD%` 0.05509 0.01285 4.285 4.06e-05 ***
`MD%`:`WA%` -0.02285 0.01265 -1.806 0.07385 .
`ERM%`:`WA%` -0.02437 0.02027 -1.202 0.23192
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 4.187 on 105 degrees of freedom
Multiple R-squared: 0.9765, Adjusted R-squared: 0.9752
F-statistic: 727.3 on 6 and 105 DF, p-value: < 2.2e-16
Call:
lm(formula = `EorM%` ~ `MD Diff SD` + `WA Diff SD` + `School Size` +
`MD Diff SD` * `School Size`, data = HSPhy_NextGen_SchoolSum)
Residuals:
Min 1Q Median 3Q Max
-40.307 -13.762 -3.628 11.108 67.074
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 72.1484 9.9200 7.273 7.10e-11 ***
`MD Diff SD` -7.1651 1.2880 -5.563 2.11e-07 ***
`WA Diff SD` 3.1782 1.2298 2.584 0.0112 *
`School Size`.L 13.4575 16.2678 0.827 0.4100
`School Size`.Q -35.9805 17.2147 -2.090 0.0391 *
`School Size`.C 20.4199 18.6382 1.096 0.2758
`MD Diff SD`:`School Size`.L -0.3028 2.2505 -0.135 0.8932
`MD Diff SD`:`School Size`.Q 5.4903 2.2503 2.440 0.0164 *
`MD Diff SD`:`School Size`.C -1.8429 2.2897 -0.805 0.4228
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 21.01 on 103 degrees of freedom
Multiple R-squared: 0.4196, Adjusted R-squared: 0.3745
F-statistic: 9.308 on 8 and 103 DF, p-value: 1.385e-09
(Intercept) `MD Diff SD` `WA Diff SD`
104.119115 -10.019434 -1.784838
`MD Diff SD`:`WA Diff SD`
0.454809
Call:
lm(formula = `EorM%` ~ (`MD Diff SD`) + `WA Diff SD` + `MD Diff SD` *
`WA Diff SD`, data = HSPhy_NextGen_SchoolSum)
Residuals:
Min 1Q Median 3Q Max
-33.160 -16.523 -5.964 14.101 69.660
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 104.1191 18.7929 5.540 2.15e-07 ***
`MD Diff SD` -10.0194 2.5033 -4.002 0.000115 ***
`WA Diff SD` -1.7848 2.1050 -0.848 0.398373
`MD Diff SD`:`WA Diff SD` 0.4548 0.2177 2.089 0.039048 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 22.18 on 108 degrees of freedom
Multiple R-squared: 0.3218, Adjusted R-squared: 0.303
F-statistic: 17.09 on 3 and 108 DF, p-value: 3.762e-09
#fit_erm = lm(`E%` ~ `ERM Diff SD`, data = HSPhy_NextGen_SchoolSum)
#summary(fit_erm)
#fit_erm_md = lm(`E%` ~ log(`MD Diff SD`) + log(`ERM Diff SD`) + log(`MD Diff SD`)*log(`ERM Diff SD`), data = HSPhy_NextGen_SchoolSum)
#summary(fit_erm_md)
#fit_md_percent = lm(`E%` ~ log(`MD%`) + log(`ERM%`) + log(`MD%`)*log(`ERM%`), data = HSPhy_NextGen_SchoolSum)
#summary(fit_md_percent)
HSPhy_NextGen_SchoolSum%>%
select(`MD%`, `E%`)
Call:
lm(formula = (`E%`) ~ log(`WA%`), data = HSPhy_NextGen_SchoolSum)
Residuals:
Min 1Q Median 3Q Max
-10.575 -5.428 -2.218 4.028 33.155
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -104.236 9.087 -11.47 <2e-16 ***
log(`WA%`) 29.999 2.408 12.46 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 7.761 on 110 degrees of freedom
Multiple R-squared: 0.5853, Adjusted R-squared: 0.5816
F-statistic: 155.3 on 1 and 110 DF, p-value: < 2.2e-16
Call:
lm(formula = (`E%`) ~ log(`MD%`), data = HSPhy_NextGen_SchoolSum)
Residuals:
Min 1Q Median 3Q Max
-11.069 -5.617 -1.981 3.093 35.895
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -93.347 8.951 -10.43 <2e-16 ***
log(`MD%`) 26.803 2.344 11.43 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 8.147 on 110 degrees of freedom
Multiple R-squared: 0.5431, Adjusted R-squared: 0.5389
F-statistic: 130.7 on 1 and 110 DF, p-value: < 2.2e-16
#fit_erm = lm(`E%` ~ `ERM Diff SD`, data = HSPhy_NextGen_SchoolSum)
#summary(fit_erm)
#fit_erm_md = lm(`E%` ~ log(`MD Diff SD`) + log(`ERM Diff SD`) + log(`MD Diff SD`)*log(`ERM Diff SD`), data = HSPhy_NextGen_SchoolSum)
#summary(fit_erm_md)
#fit_md_percent = lm(`E%` ~ log(`MD%`) + log(`ERM%`) + log(`MD%`)*log(`ERM%`), data = HSPhy_NextGen_SchoolSum)
#summary(fit_md_percent)
#HSPhy_NextGen_SchoolSum%>%
# select(`MD%`, `E%`)
ggplot(data = HSPhy_NextGen_SchoolSum, aes(x = log(`WA%`), y = log(`E%`))) +
geom_point() +
geom_smooth(method="lm", se=T)---
title: "DACSS603Final"
author: "Theresa Szczepanski"
desription: "MCAS G9 Science Analysis"
date: "10/22/2023"
format:
html:
embed-resources: true
self-contained-math: true
df-print: paged
toc: true
code-fold: true
code-copy: true
code-tools: true
bibliography: references.bib
editor:
markdown:
wrap: 72
---
```{r}
#| label: setup
#| warning: false
#| message: false
source('dependencies.R')
knitr::opts_chunk$set(echo = TRUE, warning=FALSE, message=FALSE)
#install.packages("stargazer")
library(stargazer)
```
# Research Questions
The Massachusetts Education Reform Act in 1993 was passed in the context
of a national movement toward education reform throughout the United
States. As early as 1989 there were calls to establish national
curriculum standards as a way to improve student college and career
readiness skills and close poverty gaps [@Greer18]. Massachusetts
Comprehensive Assessment System (MCAS) tests were introduced as part of
the Massachusetts Education Reform Act.
The MCAS tests are a significant tool for educational equity. Scores on
the Grade 10 Math MCAS test "predict longer-term educational attainments
and labor market success, above and beyond typical markers of student
advantage" and differences among students are largely and "sometimes
completely accounted for" by differences in 10th grade MCAS scores and
educational attainments. [@Boats20].
With the introduction of the new Common Core standards and
accountability testing came the demand for aligned curricular materials
and teaching practices. Research indicates that the choice of
instructional materials can have an impact "as large as or larger than
the impact of teacher quality" [@Blindly12]. Massachusetts, along with
Arkansas, Delaware, Kentucky, Louisiana, Maryland, Mississippi,
Nebraska, New Mexico, Ohio, Rhode Island, Tennessee, and Texas belongs
to the Council of Chief State School Officers' (CCSO), [High Quality
Instructional Materials and Professional Development
network](https://learning.ccsso.org/high-quality-instructional-materials)
which aims to close the "opportunity gap" among students by ensuring
that every teacher has access to high-quality, standards aligned
instructional materials and receives relevant professional development
to support their use of these materials [@IMPD21].
All Massachusetts Public School students must complete a High School
science MCAS exam providing a wealth of standardized data on students'
discipline specific skill development. All schools receive annual
summary reports on student performance. Significant work has been done
using the MCAS achievement data and the Student Opportunity Act to
identify achievement gaps and address funding inequities across the
Commonwealth [@Boats20]. With funding gaps outlined in the late 1990's
closing, one could consider how the MCAS data could be leveraged to
support the state's current high quality instructional materials
initiatives. The state compiles school's performance disaggregated by
each MCAS question item [@MCASIT].
Using the curricular information provided in state wide Next Generation
MCAS High School Introductory Physics Item reports together with
school-level student performance data, we hope to address the following
broad questions:
```{=html}
<style>
div.blue { background-color:#e6f0ff; border-radius: 5px; padding: 20px;}
</style>
```
::: blue
- Is there a relationship between differences in a school's
performance across Science Practice Categories and a school's
overall achievement on the Introductory Physics exam?
- How can trends in a school's performance be used to provide schools
with guidance on discipline-specific curricular areas to target to
improve student achievement?
:::
In this report, I will analyze the High School Introductory Physics Next
Generation [Massachusetts Comprehensive Assessment System
(MCAS)](https://www.doe.mass.edu/mcas/default.html) tests results for
Massachusetts public schools.
Data for the study were drawn from DESE's Next Generation MCAS Test
[Achievement Results statewide
report](https://profiles.doe.mass.edu/statereport/mcas.aspx), [Item
Analysis statewide
report](https://profiles.doe.mass.edu/statereport/nextgenmcas_item.aspx),
and the [MCAS digital item
library](https://mcas.digitalitemlibrary.com/home?subject=Science&grades=Physics&view=ALL).
The Next Generation High School Introductory Physics MCAS assessment
consists of 42 multiple choice and constructed response items that
assess students on Physical Science standards from the [2016 STE
Massachusetts Curriculum
Framework](https://www.doe.mass.edu/frameworks/scitech/2016-04.pdf) in
the content `Reporting Categories` of Motions and Forces, `MF`, Energy,
`EN`, and Waves, `WA`. Each item is associated with a specific content
standard from the Massachusetts Curriculum Framework as well as an
underlying science `Practice Category` of Evidence Reasoning and
Modeling, `ERM`, Mathematics and Data, `MD`, or Investigations and
Questioning, `IQ`. The State Item Report provides the percentage of
points earned by students in a school for each item as well as the
percentage of points earned by all students in the state for each item.
The `HSPhy_NextGen_SchoolSum` data frame contains summary performance
results from 112 public schools across the commonwealth on the Next
Generation High School Introductory Physics MCAS, which was administered
in the Spring of 2022 and 2023. 87 schools tested students in both years
and 25 schools only tested students in 1 of the 2 testing years, with
27,745 students completing the exam.
For each school, there are values reported for 44 different variables
which consist of information from three broad categories
- *School Characteristics*: This includes the name of the school and
the size of the school, `School Size`, as determined by the number
of students that completed the MCAS exam.
- *Discipline-Specifc Performance Metrics*: This includes the
percentage of points earned by students at a school for items each
content `Reporting Category`, `MF%`, `EN%`, `WA%` and science
`Practice Category` `ERM%`, `MD%`, `IQ%`, the difference between a
school's percentage of points earned compared to the percentage of
points earned by all students in the state (`MFDiff`, `ENDiff`,
etc...), and the variability in a school's performance relative to
the state by category as measured by the standard deviation of the
school's `Diff` across categories (`SD MF Diff`, `SD EN Diff`,
etc...).
- *Aggregate Performance Level metrics*: This includes a school's
percentage of students at each of the four `Performance Levels`,
(`E%`: Exceeding Expectations, `M%`: Meeting Expectations, `PM%`:
Partially Meeting Expectations, and `NM%`: Not Meeting
Expectations), the difference between these percentages and the
percentage of students in Massachusetts at each performance level
(`EDiff`, `MDiff`, `PMDiff`, `NMDiff`), and an ordinal
classification of school's, `EM Perf Stat` based on the percentage
of students that were classified as Exceeding or Meeting
expectations on the exam (`HighEM`, `HighM`, `Mid`, `Mid-Low`,
`Low`).
See the `HSPhy_NextGenMCASDF` data frame summary and **codebook** for
further details about all variables.
# Hypothesis
```{=html}
<style>
div.blue { background-color:#e6f0ff; border-radius: 5px; padding: 20px;}
</style>
```
::: blue
- A school's percentage of students classified as `Exceeding`
expectations on the Introductory Physics MCAS is negatively
associated with a school's variance in performance relative to
students in the state on `Mathematics and Data` items, `SD MD Diff`.
- A school's summary performance on items in a given content
`Reporting Category` as measured by `MF%`, `EN%`, and `WA%`, is
positively associated with the `Reporting Category's` weight within
the exam.
:::
# Descriptive Statistics
```{r}
#| label: dataframe setup
#| warning: false
#| message: false
#HSPhy_NextGen_SchoolSum
HSPhy_NextGen_SchoolSum<-HSPhy_NextGen_SchoolSum%>%
ungroup()
#HSPhy_NextGen_SchoolSum
# HSPhy_NextGen_PerfDF
# HSPhy_NextGen_SchoolIT301DF
HSPhy_2023_SchoolSizeDF<-read_excel("data/2023_Physics_NextGenMCASItem.xlsx", skip = 1)%>%
select(`School Name`, `School Code`, `Tested`)%>%
mutate(`Tested` = as.integer(`Tested`))%>%
select(`School Name`, `School Code`, `Tested`)
HSPhy_2022_SchoolSizeDF<-read_excel("data/2022_Physics_NextGenMCASItem.xlsx", skip = 1)%>%
select(`School Name`, `School Code`, `Tested`)%>%
mutate(`Tested` = as.integer(`Tested`))%>%
select(`School Name`, `School Code`, `Tested`)
HSPhy_SchoolSize <- rbind(HSPhy_2023_SchoolSizeDF, HSPhy_2022_SchoolSizeDF)%>%
mutate(count = 1)%>%
group_by(`School Name`, `School Code`)%>%
summarise(count = sum(count),
`Tested` = sum(`Tested`))%>%
mutate(`Tested Count` = round(`Tested`/count))%>%
ungroup()
#HSPhy_SchoolSize
quantile <- quantile(HSPhy_SchoolSize$`Tested Count`)
HSPhy_Size<-HSPhy_SchoolSize%>%
mutate(`School Size` = case_when(
`Tested Count` <= quantile[2] ~ "Small",
`Tested Count` > quantile[2] &
`Tested Count` <= quantile[3] ~ "Low-Mid",
`Tested Count` > quantile[3] &
`Tested Count` <= quantile[4] ~ "Upper-Mid",
`Tested Count` > quantile[4] &
`Tested Count` <= quantile[5] ~ "Large",
))%>%
mutate(`School Size` = recode_factor(`School Size`,
"Small" = "Small",
"Low-Mid" = "Low-Mid",
"Upper-Mid" = "Upper-Mid",
"Large" = "Large",
.ordered = TRUE))%>%
select(`School Name`, `School Code`, `School Size`)
#HSPhy_Size
HSPhy_NextGen_SchoolSum<-HSPhy_NextGen_SchoolSum%>%
left_join(HSPhy_Size, by = c("School Name" = "School Name", "School Code" = "School Code"))%>%
mutate(`EMDiff` = `EDiff` + `MDiff`)%>%
mutate(`EM Perf Stat` = case_when(
`EDiff` > 0 & `EDiff` + `MDiff` > 0 ~ "HighEM",
`EDiff` <= 0 & `EDiff` + `MDiff` > 0 ~ "HighM",
#`EMDiff` > quantile(HSPhy_NextGen_SchoolSum$`EMDiff`)[3] &
`EMDiff` <= 0 & `EMDiff` > -14 ~ "Mid",
`EMDiff` <= -14 & `EMDiff` >= -33 ~ "Mid-Low",
`EMDiff` < -33 ~ "Low"
))%>%
mutate(`EM Perf Stat` = recode_factor(`EM Perf Stat`,
"HighEM" = "HighEM",
"HighM" = "HighM",
"Mid" = "Mid",
"Mid-Low" = "Mid-Low",
"Low" = "Low",
.ordered = TRUE))
HSPhy_NextGen_SchoolSum
#quantile(HSPhy_NextGen_SchoolSum$`EMDiff`)
#summary(HSPhy_NextGen_SchoolSum)
print(summarytools::dfSummary(HSPhy_NextGen_SchoolSum,
varnumbers = FALSE,
plain.ascii = FALSE,
style = "grid",
graph.magnif = 0.70,
valid.col = FALSE),
method = 'render',
table.classes = 'table-condensed')
```
## Key Variables
To explore the relationship between the distribution of school's
students' `Performance Level` and school's performance in content
categories, we examine the percentage of points earned by students at
schools as well as the standard deviation of the difference between
points earned by students at a school and points earned by students in
the state across `Reporting Categories` and `Practice Categories`. We
grouped schools by their `EM Perf Stat`, an ordinal variable classifying
schools by the percentage of students they have that were classified as
either Exceeding or Meeting expectations on the MCAS. These numbers seem
to suggest that items classified with the Science `Practice Category` of
`Mathematics and Data` seem to be more challenging to students than
those classified as `Evidence, Reasoning, and Modeling`. These practice
categories are strongly and equally emphasized within the exam; items
tagged with these categories account for **82%** of the available points
on the exam with exactly **41%** of available points coming from each
category.
When considering content `Reporting Categories`, there do not seem to be
discernible distinctions between `EM Perf Stat` and school's achievement
and performance across categories. All schools seem to perform the
strongest on `Motion and Forces` items, followed by `Energy`, and
weakest on `Waves` items. Notably, this is also the order of the
relative weights of the content areas within the exam; `MF`, `EN`, and
`WA` items account for **50%**, **30%**, and **20%** of exam points
respectively.
```{r}
#quantile(HSPhy_NextGen_SchoolSum$`EMDiff`)
HSPhy_NextGen_SchoolSum%>%
group_by(`EM Perf Stat`)%>%
summarise( `Mean MD%` = mean(`MD%`),
`Mean MD SD` = mean(`MD Diff SD`),
`Mean ERM%` = mean(`ERM%`),
`Mean ERM SD` = mean (`ERM Diff SD`))
HSPhy_NextGen_SchoolSum%>%
group_by(`EM Perf Stat`)%>%
summarise( `Mean MF%` = mean(`MF%`),
`Mean MF SD` = mean(`MF Diff SD`),
`Mean EN%` = mean(`EN%`),
`Mean EN SD` = mean (`EN Diff SD`),
`Mean WA%` = mean(`WA%`),
`Mean WA SD` = mean (`WA Diff SD`)
)
```
# Visualization
## Distribution of Performance Level %
When examining the statewide performance distribution, we can see from
the right-skew that it is rare for schools to have high percentages of
students classified as `Not Meeting` expectations and even rarer for
schools to have high percentages of students classified as `Exceeding`
expectations.
```{r}
HSPhy_NextGen_SchoolSum%>%
select(`E%`, `M%`, `PM%`, `NM%`)%>%
pivot_longer(c(1:4), names_to = "Performance Level", values_to = "% Students")%>%
ggplot( aes(x=`% Students`, color=`Performance Level`, fill=`Performance Level`)) +
geom_histogram(alpha=0.6, binwidth = 15) +
scale_fill_viridis(discrete=TRUE) +
scale_color_viridis(discrete=TRUE) +
#theme_ipsum() +
theme(
legend.position="none",
panel.spacing = unit(0.1, "lines"),
strip.text.x = element_text(size = 8)
) +
facet_wrap(~`Performance Level`)+
labs( y = "",
title = "School Performance Level Distribution",
x = "% Students at Performance Level",
caption = "NextGen HS Physics MCAS")
```
## Distribution of School Performance and Variability by Practice Cat
Although `Mathematics and Data` and `Evidence, Reasoning, and Modeling`
items have strong and equal weighting in the HS Introductory Physics
exam, student performance distributions are noticeably different across
these practice categories.
```{r}
HSPhy_NextGen_SchoolSum%>%
select(`ERM%`, `MD%`)%>%
pivot_longer(c(1:2), names_to = "Practice Cat", values_to = "% Points")%>%
ggplot( aes(x=`% Points`, color=`Practice Cat`, fill=`Practice Cat`)) +
geom_histogram(alpha=0.6, binwidth = 3) +
scale_fill_viridis(discrete=TRUE) +
scale_color_viridis(discrete=TRUE) +
#theme_ipsum() +
theme(
panel.spacing = unit(0.1, "lines"),
strip.text.x = element_text(size = 8)
) +
facet_wrap(~`Practice Cat`)+
labs( y = "",
title = "School Performance by Practice Category",
x = "% Points Earned",
caption = "NextGen HS Physics MCAS")
#ggtitle("Practice Category Performance")
```
When considering the variability of a school's performance on items
relative to the state by `Practice Category`, `SD MD Diff`, and
`SD ERM Diff`, we can see that `Mathematics and Data` is skewed more to
the right.
```{r}
HSPhy_NextGen_SchoolSum%>%
select(`ERM Diff SD`, `MD Diff SD`)%>%
pivot_longer(c(1:2), names_to = "Practice Cat", values_to = "SD Diff")%>%
ggplot( aes(x=`SD Diff`, color=`Practice Cat`, fill=`Practice Cat`)) +
geom_histogram(alpha=0.6, binwidth = 3) +
scale_fill_viridis(discrete=TRUE) +
scale_color_viridis(discrete=TRUE) +
# theme_ipsum() +
theme(
panel.spacing = unit(0.1, "lines"),
strip.text.x = element_text(size = 8)
) +
labs( y = "",
title = "School Performance Variation by Practice Category",
x = "SD Diff",
caption = "NextGen HS Physics MCAS") +
facet_wrap(~`Practice Cat`)
```
## Mathematics and Data vs. Evidence Reasoning and Modeling (Practice Category)
These images, seem to suggest that schools with the **highest**
percentage of students classified as `Exceeding` expectations on the
MCAS have the **lowest** levels of variation in performance on
`Mathematics and Data` Items and schools with the **lowest** percentage
of students classified as `Exceeding` expectations on the MCAS have the
**highest** levels of variation in performance on
`Mathematics and Data Items`.
```{r}
HSPhy_NextGen_SchoolSum%>%
select(`EM Perf Stat`, `ERM Diff SD`, `MD Diff SD` )%>%
pivot_longer(c(2:3), names_to = "Practice Cat", values_to = "SD Diff")%>%
ggplot( aes(x= `EM Perf Stat`, y=`SD Diff`, fill= `EM Perf Stat`)) +
geom_boxplot() +
scale_fill_viridis(discrete = TRUE, alpha=0.6) +
geom_jitter(color="black", size=0.4, alpha=0.9) +
theme(
plot.title = element_text(size=11),
axis.title.x=element_blank(),
#axis.text.x=element_blank()
) +
labs( y = "SD Diff",
title = "Student Performance Variation by Practice Category",
x = "",
caption = "NextGen HS Physics MCAS") +
facet_wrap(~`Practice Cat`)
HSPhy_NextGen_SchoolSum%>%
select(`EM Perf Stat`, `ERM Diff SD`, `MD Diff SD` )%>%
pivot_longer(c(2:3), names_to = "Practice Cat", values_to = "SD Diff")%>%
ggplot( aes(x= `Practice Cat`, y=`SD Diff`, fill= `Practice Cat`)) +
geom_boxplot() +
scale_fill_viridis(discrete = TRUE, alpha=0.6) +
geom_jitter(color="black", size=0.4, alpha=0.9) +
#theme_ipsum() +
theme(
plot.title = element_text(size=11),
axis.title.x=element_blank(),
axis.text.x=element_blank()
) +
labs( y = "SD Diff",
title = "Student Practice Cat. Variation by Achievement Level",
x = "",
caption = "NextGen HS Physics MCAS") +
#xlab("")+
facet_wrap(~`EM Perf Stat`)
```
These images, seem to suggest that students at all schools seem to have
more difficulty with `Mathematics and Data` items as compared to
`Evidence, Reasoning, and Modeling Items`.
```{r}
HSPhy_NextGen_SchoolSum%>%
select(`EM Perf Stat`, `ERM%`, `MD%` )%>%
pivot_longer(c(2:3), names_to = "Practice Cat", values_to = "%Points")%>%
ggplot( aes(x= `EM Perf Stat`, y=`%Points`, fill= `EM Perf Stat`)) +
geom_boxplot() +
scale_fill_viridis(discrete = TRUE, alpha=0.6) +
geom_jitter(color="black", size=0.4, alpha=0.9) +
#theme_ipsum() +
theme(
plot.title = element_text(size=11)
) +
labs( y = "%Points Earned",
title = "Student Practice Cat. Achievement by Performance Level",
x = "",
caption = "NextGen HS Physics MCAS") +
#xlab("")+
facet_wrap(~`Practice Cat`)
```
```{r}
HSPhy_NextGen_SchoolSum%>%
select(`EM Perf Stat`, `ERM%`, `MD%` )%>%
pivot_longer(c(2:3), names_to = "Practice Cat", values_to = "%Points")%>%
ggplot( aes(x= `Practice Cat`, y=`%Points`, fill= `Practice Cat`)) +
geom_boxplot() +
scale_fill_viridis(discrete = TRUE, alpha=0.6) +
geom_jitter(color="black", size=0.4, alpha=0.9) +
#theme_ipsum() +
theme(
plot.title = element_text(size=11)
) +
labs( y = "%Points Earned",
title = "Student Practice Cat. Achievement by Performance Level",
x = "",
caption = "NextGen HS Physics MCAS") +
#xlab("")+
facet_wrap(~`EM Perf Stat`, scale ="free_y")
# HSPhy_NextGen_SchoolSum%>%
# select(`EM Perf Stat`, `ERMDiff`, `MDDiff` )%>%
# pivot_longer(c(2:3), names_to = "Practice Cat", values_to = "%Points")%>%
# ggplot( aes(x= `EM Perf Stat`, y=`%Points`, fill= `EM Perf Stat`)) +
# geom_boxplot() +
# scale_fill_viridis(discrete = TRUE, alpha=0.6) +
# geom_jitter(color="black", size=0.4, alpha=0.9) +
# #theme_ipsum() +
# theme(
#
# plot.title = element_text(size=11)
# ) +
# labs( y = "%Points Earned",
# title = "Student Practice Cat. Achievement by Performance Level",
# x = "",
# caption = "NextGen HS Physics MCAS") +
# #xlab("")+
# facet_wrap(~`Practice Cat`)
# HSPhy_NextGen_SchoolSum%>%
# select(`EM Perf Stat`, `ERM%`, `MD%` )%>%
# pivot_longer(c(2:3), names_to = "Practice Cat", values_to = "%Points")%>%
# ggplot( aes(x= `Practice Cat`, y=`%Points`, fill= `Practice Cat`)) +
# geom_boxplot() +
# scale_fill_viridis(discrete = TRUE, alpha=0.6) +
# geom_jitter(color="black", size=0.4, alpha=0.9) +
# #theme_ipsum() +
# theme(
#
# plot.title = element_text(size=11)
# ) +
# labs( y = "%Points Earned",
# title = "Student Practice Cat. Achievement by Performance Level",
# x = "",
# caption = "NextGen HS Physics MCAS") +
# #xlab("")+
# facet_wrap(~`EM Perf Stat`, scale ="free_y")
# HSPhy_NextGen_SchoolSum %>%
# ggplot( aes(x= `EM Perf Stat`, y=`MD%`, fill= `EM Perf Stat`)) +
# geom_boxplot() +
# scale_fill_viridis(discrete = TRUE, alpha=0.6) +
# geom_jitter(color="black", size=0.4, alpha=0.9) +
# theme_ipsum() +
# theme(
# legend.position="none",
# plot.title = element_text(size=11)
# ) +
# ggtitle("A boxplot with jitter") +
# xlab("")
# HSPhy_NextGen_SchoolSum %>%
# ggplot( aes(x= `EM Perf Stat`, y=`MD Diff SD`, fill= `EM Perf Stat`)) +
# geom_boxplot() +
# scale_fill_viridis(discrete = TRUE, alpha=0.6) +
# geom_jitter(color="black", size=0.4, alpha=0.9) +
# theme_ipsum() +
# theme(
# legend.position="none",
# plot.title = element_text(size=11)
# ) +
# ggtitle("A boxplot with jitter") +
# xlab("")
#
# HSPhy_NextGen_SchoolSum %>%
# ggplot( aes(x= `EM Perf Stat`, y=`ERM Diff SD`, fill= `EM Perf Stat`)) +
# geom_boxplot() +
# scale_fill_viridis(discrete = TRUE, alpha=0.6) +
# geom_jitter(color="black", size=0.4, alpha=0.9) +
# theme_ipsum() +
# theme(
# legend.position="none",
# plot.title = element_text(size=11)
# ) +
# ggtitle("A boxplot with jitter") +
# xlab("")
#
# HSPhy_NextGen_SchoolSum %>%
# ggplot( aes(x= `EM Perf Stat`, y=`ERM%`, fill= `EM Perf Stat`)) +
# geom_boxplot() +
# scale_fill_viridis(discrete = TRUE, alpha=0.6) +
# geom_jitter(color="black", size=0.4, alpha=0.9) +
# theme_ipsum() +
# theme(
# legend.position="none",
# plot.title = element_text(size=11)
# ) +
# ggtitle("A boxplot with jitter") +
# xlab("")
```
## Distribution of School Performance and Variability by Reporting Cat
Here we can visualize the variability of a school's performance on items
partitioned by Content `Reporting Category` of `Motion and Forces`,
`Energy`, and `Waves` via: `MF%`/`SD MF Diff`, `EN%`/`SD EN Diff`, and
`WA%`/`SD WA Diff`.
```{r}
HSPhy_NextGen_SchoolSum%>%
select(`EM Perf Stat`, `MF Diff SD`, `EN Diff SD`, `WA Diff SD` )%>%
pivot_longer(c(2:4), names_to = "Report Cat", values_to = "SD Diff")%>%
ggplot( aes(x=`SD Diff`, color=`Report Cat`, fill=`Report Cat`)) +
geom_histogram(alpha=0.6, binwidth = 3) +
scale_fill_viridis(discrete=TRUE) +
scale_color_viridis(discrete=TRUE) +
#theme_ipsum() +
theme(
panel.spacing = unit(0.1, "lines"),
strip.text.x = element_text(size = 8)
) +
labs( y = "",
title = "School Performance Variation by Content Reporting Category",
x = "SD Diff",
caption = "NextGen HS Physics MCAS") +
facet_wrap(~`Report Cat`)
```
```{r}
HSPhy_NextGen_SchoolSum%>%
select(`EM Perf Stat`, `MF%`, `EN%`, `WA%` )%>%
pivot_longer(c(2:4), names_to = "Report Cat", values_to = "% Points")%>%
ggplot( aes(x=`% Points`, color=`Report Cat`, fill=`Report Cat`)) +
geom_histogram(alpha=0.6, binwidth = 3) +
scale_fill_viridis(discrete=TRUE) +
scale_color_viridis(discrete=TRUE) +
#theme_ipsum() +
theme(
panel.spacing = unit(0.1, "lines"),
strip.text.x = element_text(size = 8)
) +
facet_wrap(~`Report Cat`)+
labs( y = "",
title = "Student Performance by Content Reporting Category",
x = "% Points Earned",
caption = "NextGen HS Physics MCAS")
#ggtitle("Practice Category Performance")
```
## Motion and Forces vs. Energy vs. Waves (Reporting Category)
These images suggest that most schools exhibit similar levels of
variability in performance relative to the state across all reporting
categories. Schools with the ***lowest percentage*** of students
`Exceeding` expectations exhibit ***high variability*** in performance
across all content reporting categories, but seem to have lower
variability on `Waves` items.
```{r}
HSPhy_NextGen_SchoolSum%>%
select(`EM Perf Stat`, `MF Diff SD`, `EN Diff SD`, `WA Diff SD` )%>%
pivot_longer(c(2:4), names_to = "Report Cat", values_to = "SD Diff")%>%
ggplot( aes(x= `EM Perf Stat`, y=`SD Diff`, fill= `EM Perf Stat`)) +
geom_boxplot() +
scale_fill_viridis(discrete = TRUE, alpha=0.6) +
geom_jitter(color="black", size=0.4, alpha=0.9) +
theme(
plot.title = element_text(size=11),
axis.title.x=element_blank(),
axis.text.x=element_blank()
) +
labs( y = "SD Diff",
title = "School Performance Variation by Content Reporting Category",
x = "",
caption = "NextGen HS Physics MCAS") +
facet_wrap(~`Report Cat`)
HSPhy_NextGen_SchoolSum%>%
select(`EM Perf Stat`, `MF Diff SD`, `EN Diff SD`, `WA Diff SD` )%>%
pivot_longer(c(2:4), names_to = "Report Cat", values_to = "SD Diff")%>%
ggplot( aes(x= `Report Cat`, y=`SD Diff`, fill= `Report Cat`)) +
geom_boxplot() +
scale_fill_viridis(discrete = TRUE, alpha=0.6) +
geom_jitter(color="black", size=0.4, alpha=0.9) +
#theme_ipsum() +
theme(
plot.title = element_text(size=11),
axis.title.x=element_blank(),
axis.text.x=element_blank()
) +
labs( y = "SD Diff",
title = "School Content Reporting Cat. Variation by Achievement Level",
x = "",
caption = "NextGen HS Physics MCAS") +
#xlab("")+
facet_wrap(~`EM Perf Stat`)
HSPhy_NextGen_SchoolSum%>%
select(`EM Perf Stat`, `MF%`, `EN%`, `WA%` )%>%
pivot_longer(c(2:4), names_to = "Report Cat", values_to = "% Points")%>%
ggplot( aes(x= `Report Cat`, y=`% Points`, fill= `Report Cat`)) +
geom_boxplot() +
scale_fill_viridis(discrete = TRUE, alpha=0.6) +
geom_jitter(color="black", size=0.4, alpha=0.9) +
#theme_ipsum() +
theme(
plot.title = element_text(size=11),
axis.title.x=element_blank(),
axis.text.x=element_blank()
) +
labs( y = "Report Cat%",
title = "School Content Reporting Cat. Performance by Achievement Level",
x = "",
caption = "NextGen HS Physics MCAS") +
#xlab("")+
facet_wrap(~`EM Perf Stat`)
# HSPhy_NextGen_SchoolSum %>%
# ggplot( aes(x= `EM Perf Stat`, y=`MF%`, fill= `EM Perf Stat`)) +
# geom_boxplot() +
# scale_fill_viridis(discrete = TRUE, alpha=0.6) +
# geom_jitter(color="black", size=0.4, alpha=0.9) +
# theme_ipsum() +
# theme(
# legend.position="none",
# plot.title = element_text(size=11)
# ) +
# ggtitle("A boxplot with jitter") +
# xlab("")
#
# HSPhy_NextGen_SchoolSum %>%
# ggplot( aes(x= `EM Perf Stat`, y=`MF Diff SD`, fill= `EM Perf Stat`)) +
# geom_boxplot() +
# scale_fill_viridis(discrete = TRUE, alpha=0.6) +
# geom_jitter(color="black", size=0.4, alpha=0.9) +
# theme_ipsum() +
# theme(
# legend.position="none",
# plot.title = element_text(size=11)
# ) +
# ggtitle("A boxplot with jitter") +
# xlab("")
#
#
#
# HSPhy_NextGen_SchoolSum %>%
# ggplot( aes(x= `EM Perf Stat`, y=`EN%`, fill= `EM Perf Stat`)) +
# geom_boxplot() +
# scale_fill_viridis(discrete = TRUE, alpha=0.6) +
# geom_jitter(color="black", size=0.4, alpha=0.9) +
# theme_ipsum() +
# theme(
# legend.position="none",
# plot.title = element_text(size=11)
# ) +
# ggtitle("A boxplot with jitter") +
# xlab("")
#
# HSPhy_NextGen_SchoolSum %>%
# ggplot( aes(x= `EM Perf Stat`, y=`EN Diff SD`, fill= `EM Perf Stat`)) +
# geom_boxplot() +
# scale_fill_viridis(discrete = TRUE, alpha=0.6) +
# geom_jitter(color="black", size=0.4, alpha=0.9) +
# theme_ipsum() +
# theme(
# legend.position="none",
# plot.title = element_text(size=11)
# ) +
# ggtitle("A boxplot with jitter") +
# xlab("")
#
# HSPhy_NextGen_SchoolSum %>%
# ggplot( aes(x= `EM Perf Stat`, y=`WA%`, fill= `EM Perf Stat`)) +
# geom_boxplot() +
# scale_fill_viridis(discrete = TRUE, alpha=0.6) +
# geom_jitter(color="black", size=0.4, alpha=0.9) +
# theme_ipsum() +
# theme(
# legend.position="none",
# plot.title = element_text(size=11)
# ) +
# ggtitle("A boxplot with jitter") +
# xlab("")
#
# HSPhy_NextGen_SchoolSum %>%
# ggplot( aes(x= `EM Perf Stat`, y=`WA Diff SD`, fill= `EM Perf Stat`)) +
# geom_boxplot() +
# scale_fill_viridis(discrete = TRUE, alpha=0.6) +
# geom_jitter(color="black", size=0.4, alpha=0.9) +
# theme_ipsum() +
# theme(
# legend.position="none",
# plot.title = element_text(size=11)
# ) +
# ggtitle("A boxplot with jitter") +
# xlab("")
```
# Hypothesis Testing
## Hypothesis 1: Variation in Mathematics
```{=html}
<style>
div.blue { background-color:#e6f0ff; border-radius: 5px; padding: 20px;}
</style>
```
::: blue
- A school's percentage of students classified as `Exceeding or Meeting`
expectations on the Introductory Physics MCAS is negatively
associated with a school's variance in performance relative to
students in the state on `Mathematics and Data` items, `SD MD Diff`.
:::
```{r}
HSPhy_NextGen_SchoolSum<-HSPhy_NextGen_SchoolSum%>%
ungroup()
HSPhy_NextGen_SchoolSum<-HSPhy_NextGen_SchoolSum%>%
mutate(`EorM%` = `E%` + `M%`)
HSPhy_NextGen_SchoolSum
```
### Anova: SD-Diff MD
To explore the relationship between the variance in a schools' `Diff` compared to the state on Mathematics and Data items, `MD Diff SD` and a school's percentage of students meeting or exceeding expectations on the MCAS, `EorM%`, we ran a few Hypothesis tests. We considered the impact of the variability in `Evidence, Reasoning, and Modeling`, `ERM Diff SD`, and `School Size` as controls. From our table, there appears to be a relationship between `School Size`. It appears that `Small` schools have a higher variation in mathematics and data items and typically perform worse on Mathematics and Data and overall on the MCAS compared to larger schools.
```{r}
HSPhy_NextGen_SchoolSum%>%
group_by(`School Size`)%>%
summarize(
`Mean EorM%` = mean(`EorM%`),
`Mean MD%` = mean(`MD%`),
`Mean MD Diff SD` = mean(`MD Diff SD`),
`Mean ERM%` = mean(`ERM%`),
`Mean ERM Diff SD` = mean(`ERM Diff SD`)
)
```
```{r}
HSPhy_NextGen_SchoolSum%>%
select(`School Size`, `MD Diff SD`, `ERM Diff SD` )%>%
pivot_longer(c(2:3), names_to = "Practice Cat", values_to = "SD Diff")%>%
ggplot( aes(x= `Practice Cat`, y=`SD Diff`, fill= `Practice Cat`)) +
geom_boxplot() +
scale_fill_viridis(discrete = TRUE, alpha=0.6) +
geom_jitter(color="black", size=0.4, alpha=0.9) +
#theme_ipsum() +
theme(
plot.title = element_text(size=11),
axis.title.x=element_blank(),
axis.text.x=element_blank()
) +
labs( y = "SD Diff",
title = "Student Practice Cat. Variation by School Size",
x = "",
caption = "NextGen HS Physics MCAS") +
#xlab("")+
facet_wrap(~`School Size`, scale = "free")
HSPhy_NextGen_SchoolSum%>%
select(`School Size`, `MD%`, `ERM%` )%>%
pivot_longer(c(2:3), names_to = "Practice Cat", values_to = "%Points")%>%
ggplot( aes(x= `Practice Cat`, y=`%Points`, fill= `Practice Cat`)) +
geom_boxplot() +
scale_fill_viridis(discrete = TRUE, alpha=0.6) +
geom_jitter(color="black", size=0.4, alpha=0.9) +
#theme_ipsum() +
theme(
plot.title = element_text(size=11),
axis.title.x=element_blank(),
axis.text.x=element_blank()
) +
labs( y = "% Points Earned",
title = "Student Practice Cat. Achievement by School Size",
x = "",
caption = "NextGen HS Physics MCAS") +
#xlab("")+
facet_wrap(~`School Size`)
```
However, when you group the schools by `EM Perf Stat`, you find that the highest performing, `High EM`, `Small` schools have a higher percentage of students meeting or exceeding expectations.
Across all sizes, it seems that the weakest performing schools have more variation in mathematics and data and the strongest performing schools have less variability in `Mathematics and Data` than in `Evidence, Reasoning, and Modeling`.
```{r}
# Faceted by performance level
HSPhy_NextGen_SchoolSum%>%
group_by(`School Size`, `EM Perf Stat`)%>%
summarize(`Mean EorM%` = mean(`EorM%`),
`Mean MD%` = mean(`MD%`),
`Mean MD Diff SD` = mean(`MD Diff SD`),
`Mean ERM%` = mean(`ERM%`),
`Mean ERM Diff SD` = mean(`ERM Diff SD`)
)
HSPhy_NextGen_SchoolSum%>%
select(`School Size`, `EorM%`, `MD Diff SD`, `EM Perf Stat` )%>%
#pivot_longer(c(2:3), names_to = "Practice Cat", values_to = "SD Diff")%>%
ggplot( aes(x= `School Size`, y=`EorM%`, fill= `School Size`)) +
geom_boxplot() +
scale_fill_viridis(discrete = TRUE, alpha=0.6) +
geom_jitter(color="black", size=0.4, alpha=0.9) +
#theme_ipsum() +
theme(
plot.title = element_text(size=11),
axis.title.x=element_blank(),
axis.text.x=element_blank()
) +
labs( y = "SD Diff",
title = "Students Meeting or Exceeding Expectations . Variation by Achievement Level",
x = "",
caption = "NextGen HS Physics MCAS") +
#xlab("")+
facet_wrap(~`EM Perf Stat`, scales = "free")
```
```{r}
ANOVA_MD_size <- aov(`MD Diff SD` ~ `EM Perf Stat` + `School Size`, data=HSPhy_NextGen_SchoolSum)
ANOVA_MD_interact <- aov(`MD Diff SD` ~ `EM Perf Stat` + `School Size` + `EM Perf Stat` * `School Size`, data=HSPhy_NextGen_SchoolSum)
ANOVA_EorM_MD<- aov(`EorM%` ~ `MD Diff SD` + `School Size`, data=HSPhy_NextGen_SchoolSum)
ANOVA_EorM_interact_MD <- aov(`EorM%` ~ `MD Diff SD` + `School Size` + `MD Diff SD` * `School Size`, data=HSPhy_NextGen_SchoolSum)
summary(ANOVA_MD_size)
summary(ANOVA_MD_interact)
summary(ANOVA_EorM_MD)
summary(ANOVA_EorM_interact_MD)
HSPhy_NextGen_SchoolSum%>%
group_by(`School Size`, `EM Perf Stat`)%>%
summarize(`Mean MD%` = mean(`MD%`),
`Mean MD Diff SD` = mean(`MD Diff SD`),
`Mean ERM%` = mean(`ERM%`),
`Mean ERM Diff SD` = mean(`ERM Diff SD`)
)
HSPhy_NextGen_SchoolSum%>%
group_by(`School Size`)%>%
summarize(
`Mean EorM%` = mean(`EorM%`),
`Mean MD%` = mean(`MD%`),
`Mean MD Diff SD` = mean(`MD Diff SD`),
`Mean ERM%` = mean(`ERM%`),
`Mean ERM Diff SD` = mean(`ERM Diff SD`)
)
HSPhy_NextGen_SchoolSum%>%
group_by(`School Size`, `EM Perf Stat`)%>%
summarize(`Mean EorM%` = mean(`EorM%`),
`Mean MD%` = mean(`MD%`),
`Mean MD Diff SD` = mean(`MD Diff SD`),
`Mean ERM%` = mean(`ERM%`),
`Mean ERM Diff SD` = mean(`ERM Diff SD`)
)
HSPhy_NextGen_SchoolSum%>%
filter(`School Size` == "Small")
```
## ANOVA SD-Diff ERM
```{r}
ANOVA_ERM <- aov(`ERM Diff SD` ~ `EM Perf Stat`, data=HSPhy_NextGen_SchoolSum)
ANOVA_ERM_Size <- aov(`ERM Diff SD` ~ `EM Perf Stat` + `School Size`, data=HSPhy_NextGen_SchoolSum)
summary(ANOVA_ERM)
summary(ANOVA_ERM_Size)
ANOVA_EorM_ERM<- aov(`EorM%` ~ `ERM Diff SD` + `School Size`, data=HSPhy_NextGen_SchoolSum)
ANOVA_EorM_interact_ERM <- aov(`EorM%` ~ `ERM Diff SD` + `School Size` + `ERM Diff SD` * `School Size`, data=HSPhy_NextGen_SchoolSum)
summary(ANOVA_EorM_ERM)
summary(ANOVA_EorM_interact_ERM)
```
## SD-Diff MD + ERM
```{r}
ANOVA_EorM_MD_ERM <- aov(`EorM%` ~ `MD Diff SD` + `ERM Diff SD`, data=HSPhy_NextGen_SchoolSum)
summary(ANOVA_EorM_MD_ERM)
```
## T Test EM Diff SD vs. MD Diff SD
```{r}
HSPhy_NextGen_SchoolSum_Diff<-HSPhy_NextGen_SchoolSum %>%
select(`EM Perf Stat`, `ERM Diff SD`, `MD Diff SD` )%>%
pivot_longer(c(2:3), names_to = "Practice Cat", values_to = "SD Diff")%>%
group_by(`Practice Cat`, `EM Perf Stat`)%>%
summarize(`SD SD Diff` = sd(`SD Diff`, na.rm = TRUE),
`Mean SD Diff` = mean(`SD Diff`, na.rm = TRUE))%>%
ungroup()
test1 <- HSPhy_NextGen_SchoolSum_Diff%>%
select(`Practice Cat`, `SD SD Diff`)
t.test( test1$`SD SD Diff` ~ test1$`Practice Cat`, paired = TRUE)
test2<-HSPhy_NextGen_SchoolSum %>%
select(`School Name`, `EM Perf Stat`, `School Size`, `ERM Diff SD`, `MD Diff SD` )%>%
pivot_longer(c(4:5), names_to = "Practice Cat", values_to = "SD Diff")%>%
filter(`EM Perf Stat` == "HighEM" | `EM Perf Stat` == "Mid")
## filtered for High Performing Schools
test2
t.test(test2$`SD Diff`~ test2$`Practice Cat`, paired = TRUE)
test3<-HSPhy_NextGen_SchoolSum %>%
select(`School Name`, `EM Perf Stat`, `School Size`, `ERM Diff SD`, `MD Diff SD` )%>%
pivot_longer(c(4:5), names_to = "Practice Cat", values_to = "SD Diff")%>%
filter(`EM Perf Stat` == "Low")
## filtered for High Performing Schools
test3
t.test(test3$`SD Diff`~ test3$`Practice Cat`, paired = TRUE)
```
## Hypothesis 2: Reporting Cateogy and School Performance
```{=html}
<style>
div.blue { background-color:#e6f0ff; border-radius: 5px; padding: 20px;}
</style>
```
::: blue
- A school's summary performance on items in a given content
`Reporting Category` as measured by `MF%`, `EN%`, and `WA%`, is
positively associated with the `Reporting Category's` weight within
the exam.
:::
## SD-Diff Reporting Categories
```{r}
ANOVA_WA <- aov(`WA Diff SD` ~ `EM Perf Stat`, data=HSPhy_NextGen_SchoolSum)
summary(ANOVA_WA)
ANOVA_EN <- aov(`EN Diff SD` ~ `EM Perf Stat`, data=HSPhy_NextGen_SchoolSum)
summary(ANOVA_EN)
ANOVA_MF <- aov(`MF Diff SD` ~ `EM Perf Stat`, data=HSPhy_NextGen_SchoolSum)
summary(ANOVA_MF)
HSPhy_NextGen_SchoolSum%>%
select(`EM Perf Stat`, `MF Diff SD`, `EN Diff SD`, `WA Diff SD` )%>%
pivot_longer(c(2:4), names_to = "Report Cat", values_to = "SD Diff")%>%
group_by(`Report Cat`, `EM Perf Stat`)%>%
summarize(`SD SD Diff` = sd(`SD Diff`, na.rm = TRUE))
HSPhy_NextGen_SchoolSum%>%
select(`EM Perf Stat`, `ERM Diff SD`, `MD Diff SD` )%>%
pivot_longer(c(2:3), names_to = "Practice Cat", values_to = "SD Diff")%>%
group_by(`Practice Cat`, `EM Perf Stat`)%>%
summarize(`SD SD Diff` = sd(`SD Diff`, na.rm = TRUE),
`Mean SD Diff` = mean(`SD Diff`, na.rm = TRUE))
```
## Visualizations
```{r}
ggplot(data = HSPhy_NextGen_SchoolSum, aes(x = `ERM Diff SD`, y = (`EorM%`))) +
geom_point() +
geom_smooth(method="lm", se=T)
ggplot(data = HSPhy_NextGen_SchoolSum, aes(x = `MD Diff SD`, y = (`EorM%`))) +
geom_point() +
geom_smooth(method="lm", se=T)
ggplot(data = HSPhy_NextGen_SchoolSum, aes(x = `MD Diff SD`, y = (`E%`))) +
geom_point() +
geom_smooth(method="lm", se=T)
ggplot(data = HSPhy_NextGen_SchoolSum, aes(x = `ERM Diff SD`, y = (`E%`))) +
geom_point() +
geom_smooth(method="lm", se=T)
ggplot(data = HSPhy_NextGen_SchoolSum, aes(x = (`WA Diff SD`), y = ((`E%`)))) +
geom_point() +
geom_smooth(method="lm", se=T)
```
## MD Diff Alone
```{r}
fit_md = lm(`EorM%` ~ (`MD Diff SD`), data = HSPhy_NextGen_SchoolSum)
summary(fit_md)
```
## MD and ERM Diff
This states that MD is significant but ERM is not statistically
significant?
```{r}
fit_md_erm = lm(`EorM%` ~ (`ERM Diff SD` + `MD Diff SD`), data = HSPhy_NextGen_SchoolSum)
summary(fit_md_erm)
```
## Reporting Category DIFF alone and with interactions
### EN
```{r}
fit_en = lm(`EorM%` ~ (`EN Diff SD`), data = HSPhy_NextGen_SchoolSum)
summary(fit_en)
```
### MF
```{r}
fit_mf = lm(`EorM%` ~ (`MF Diff SD`), data = HSPhy_NextGen_SchoolSum)
summary(fit_mf)
```
### WA
```{r}
fit_wa = lm(`EorM%` ~ (`WA Diff SD`), data = HSPhy_NextGen_SchoolSum)
summary(fit_wa)
```
### MF/EN
```{r}
fit_mf_en = lm(`EorM%` ~ (`MF Diff SD`) + `EN Diff SD` + `MF Diff SD`*`EN Diff SD`, data = HSPhy_NextGen_SchoolSum)
summary(fit_mf_en)
```
### MF/WA
```{r}
fit_mf_wa = lm(`EorM%` ~ (`MF Diff SD`) + `WA Diff SD` + `MF Diff SD`*`WA Diff SD`, data = HSPhy_NextGen_SchoolSum)
summary(fit_mf_wa)
```
## Practice Cat Interacting with Reporting Cat
### MD/WA
```{r}
fit_md_wa = lm(`EorM%` ~ (`MD Diff SD`) + `WA Diff SD` + `MD Diff SD`*`WA Diff SD`, data = HSPhy_NextGen_SchoolSum)
summary(fit_md_wa)
```
### MD/MF
```{r}
fit_md_mf = lm(`EorM%` ~ (`MD Diff SD`) + `MF Diff SD` + `MD Diff SD`*`MF Diff SD`, data = HSPhy_NextGen_SchoolSum)
summary(fit_md_mf)
```
### MD/EN
```{r}
fit_md_en = lm(`EorM%` ~ (`MD Diff SD`) + `EN Diff SD` + `MD Diff SD`*`EN Diff SD`, data = HSPhy_NextGen_SchoolSum)
summary(fit_md_en)
```
## Practice Cat %
### MD/ERM
```{r}
fit_md_erm_percent = lm(`EorM%` ~ `MD%` + `ERM%` + `MD%`*`ERM%`, data = HSPhy_NextGen_SchoolSum)
summary(fit_md_erm_percent)
```
### MD/WA
```{r}
fit_md_wa_percent = lm(`EorM%` ~ `MD%` + `WA%` + `MD%`*`WA%`, data = HSPhy_NextGen_SchoolSum)
summary(fit_md_wa_percent)
```
### ERM/WA
```{r}
fit_erm_wa_percent = lm(`EorM%` ~ `ERM%` + `WA%` + `ERM%`*`WA%`, data = HSPhy_NextGen_SchoolSum)
summary(fit_erm_wa_percent)
```
### MD, ERM, MF
```{r}
fit_md_erm_mf_percent = lm(`EorM%` ~ `ERM%` + `MD%` + `MF%` + `MD%`*`ERM%`+ `MD%`*`MF%` + `ERM%`*`MF%`, data = HSPhy_NextGen_SchoolSum)
summary(fit_md_erm_mf_percent)
```
### MD, ERM, WA
```{r}
fit_md_erm_wa_percent = lm(`EorM%` ~ `ERM%` + `MD%` + `WA%` + `MD%`*`ERM%`+ `MD%`*`WA%` + `ERM%`*`WA%`, data = HSPhy_NextGen_SchoolSum)
summary(fit_md_erm_wa_percent)
```
## MD-Diff, WA Diff, and School Size
```{r}
fit_md_wa_size = lm(`EorM%` ~ `MD Diff SD` + `WA Diff SD` + `School Size` + `MD Diff SD`*`School Size`, data = HSPhy_NextGen_SchoolSum)
summary(fit_md_wa_size)
HSPhy_NextGen_SchoolSum
```
# Scatter Plots
## MD + WA
```{r}
fit_md_wa$coefficients
summary(fit_md_wa)
ggplot(data = HSPhy_NextGen_SchoolSum, aes(x = -10.019434*`MD Diff SD` + -1.7848*`WA Diff SD` + 0.4548*`MD Diff SD`*`WA Diff SD` + 104.1191, y = `EorM%`)) +
geom_point() +
geom_smooth(method="lm", se=T)
ggplot(data = HSPhy_NextGen_SchoolSum, aes(x = `MD Diff SD` + `WA Diff SD`, y = `EorM%`)) +
geom_point() +
geom_smooth(method="lm", se=T)
```
```{r}
ggplot(data = HSPhy_NextGen_SchoolSum, aes(x = 1.290583*`MD%` + -0.015233*`WA%` + 0.006053*`WA%`*`MD%` + -35.163765 , y = `EorM%`)) +
geom_point() +
geom_smooth(method="lm", se=T)
```
```{r}
#fit_erm = lm(`E%` ~ `ERM Diff SD`, data = HSPhy_NextGen_SchoolSum)
#summary(fit_erm)
#fit_erm_md = lm(`E%` ~ log(`MD Diff SD`) + log(`ERM Diff SD`) + log(`MD Diff SD`)*log(`ERM Diff SD`), data = HSPhy_NextGen_SchoolSum)
#summary(fit_erm_md)
#fit_md_percent = lm(`E%` ~ log(`MD%`) + log(`ERM%`) + log(`MD%`)*log(`ERM%`), data = HSPhy_NextGen_SchoolSum)
#summary(fit_md_percent)
HSPhy_NextGen_SchoolSum%>%
select(`MD%`, `E%`)
ggplot(data = HSPhy_NextGen_SchoolSum, aes(x = `MD%`, y = log(`E%`))) +
geom_point() +
geom_smooth(method="lm", se=T)
ggplot(data = HSPhy_NextGen_SchoolSum, aes(x = `ERM%`, y = log(`E%`))) +
geom_point() +
geom_smooth(method="lm", se=T)
ggplot(data = HSPhy_NextGen_SchoolSum, aes(x = log(`MD Diff SD`), y = (`E%`))) +
geom_point() +
geom_smooth(method="lm", se=T)
```
```{r}
#HSPhy_NextGen_SchoolSum.isna()
fit_wa = lm((`E%`) ~ log(`WA%`), data = HSPhy_NextGen_SchoolSum)
summary(fit_wa)
fit_md = lm((`E%`) ~ log(`MD%`), data = HSPhy_NextGen_SchoolSum)
summary(fit_md)
#fit_erm = lm(`E%` ~ `ERM Diff SD`, data = HSPhy_NextGen_SchoolSum)
#summary(fit_erm)
#fit_erm_md = lm(`E%` ~ log(`MD Diff SD`) + log(`ERM Diff SD`) + log(`MD Diff SD`)*log(`ERM Diff SD`), data = HSPhy_NextGen_SchoolSum)
#summary(fit_erm_md)
#fit_md_percent = lm(`E%` ~ log(`MD%`) + log(`ERM%`) + log(`MD%`)*log(`ERM%`), data = HSPhy_NextGen_SchoolSum)
#summary(fit_md_percent)
#HSPhy_NextGen_SchoolSum%>%
# select(`MD%`, `E%`)
ggplot(data = HSPhy_NextGen_SchoolSum, aes(x = log(`WA%`), y = log(`E%`))) +
geom_point() +
geom_smooth(method="lm", se=T)
#ggplot(data = HSPhy_NextGen_SchoolSum, aes(x = `ERM%`, y = log(`E%`))) +
# geom_point() +
# geom_smooth(method="lm", se=T)
#ggplot(data = HSPhy_NextGen_SchoolSum, aes(x = log(`MD Diff SD`), y = (`E%`))) +
# geom_point() +
# geom_smooth(method="lm", se=T)
```
# References